EP0787514A2 - Stereometric toy, stereometric shape, in particular stereometric toy - Google Patents

Abstract

A closable or enclosed chain is made of polyhedrons hinged together. It makes up a stereometric body, particularly a toy, which can be put into several spatial shapes, each different from the others. At least one of these shapes, the basic setting, forms a regular body, the surfaces of which are each formed of a surface of a polyhedron. The body may have the basic form of a cube (10), such that at least one surface of the cube is formed by polyhedron surfaces (e.g. EFHO) which belong to polyhedrons which are not immediately adjacent in the polyhedron chain or ring. At least one further spatial shape is a ring, through which a cube in the basic setting can be passed.

Description

The invention relates to a stereometric structure, in particular a stereometric toy, with a chain that can be closed or closed to form a ring of articulated polyhedra. The structure can be brought into several different spatial forms.

Such a stereometric toy is known from "Paul Schatz, rhythm research and technology, Verlag Freies Geistesleben, 1975".

Stereometric toys are generally spatial toys, in which play can be played by changing or varying a plurality of physical structures. A simple example of such a stereometric toy is the classic wooden construction kit. Particularly attractive stereometric toys of this type are known from Naef AG, "naef collection", 1995.

From DE 90 16 309 U1 a spatial logic toy consisting of several elements is also known. The logic toy consists of individual toy elements that can be attached to one another at contact surfaces and which can form an imaginary lattice work in the form of a regular or semi-regular body. However, this toy does not form a closed unit, so that there is a risk that individual elements can be lost.

From "Doris Schattschneider and Wallis Walker, MG Escher kaleidocycles, TACO Verlagsgesellschaft and Agentur mbH, 1987", three-dimensional rings made of tetrahedra (known as kaleidocycles) are known. Several identical tetrahedra will be assembled into a chain by flexibly connecting two tetrahedra at one edge. As soon as this chain is long enough, it can be put together in a closed circle. Because of the flexible hinges on the edges, the ring can be turned continuously through its center. These kaleidocycles thus essentially have a ring shape, the shape of which varies in the course of the rotation through its center and thereby gives an impression similar to the opening of a flower. These kaleidocycles are therefore visually very appealing, but the degrees of freedom in handling are limited to rotating the ring formed from the tetrahedra either inwards or outwards.

A reversible cube belt is known from the above-mentioned publication "Paul Schatz, rhythm research and technology, Verlag Freies Geistesleben, 1975". The cube belt is created by taking two mutually penetrating star body bars from a cube. The remaining cube belt consists essentially of six four-sided bodies, which are connected to each other in an articulated manner to form a ring. The cube belt can be turned inside out, so that - similar to the previously mentioned kaleidocycles - different spatial shapes can be formed, the shape of which resembles, for example, a star shape or a ring shape. The order of the spatial shapes created during the inversion process is inevitable, so that the cube belt quickly becomes uninteresting as a game.

"Invertible models of the Platonic solids", published by the workshop for Platonic solids, further known reversible models of Platonic solids are known. These models have in common that - similar to the cube belt described above - the platonic body is composed of several individual bodies, one of which is formed by an articulated chain of polyhedra. This chain of polyhedra can be connected to form a ring that can be turned inside out.

From GB-OS 2 108 395 a polyhedron ring is known which is a cube in its basic position. However, only 6 of its 12 polyhedron edge connections lie on cube edges, the other 6 on diagonals of the cube. Furthermore, all surfaces of the cube are formed by polyhedron surfaces that belong to polyhedra that are immediately adjacent in the polyhedron ring. This results in a loosened form of a wide-opening 12-membered polyhedron ring, which, however, is designed less uniformly due to the mutual nature of the formation of the polyhedron compounds and, from a playful point of view, only challenges the interest for a short time due to its simple kinematic inversion behavior.

Another cube is known from GB-OS 2 111 395, which has inverted properties. The inversion process is, however, completely determined by the choice of the axes of movement between the polyhedra, so that there is also no longer-term interesting game from this design. Furthermore, the cube can only be opened to a ring with a very small opening.

Finally, the stereometric toys also include the well-known logic toys, such as the Rubik's cube, which has several elements which, although connected to form a closed arrangement, can change their relative positions to one another. The logic task with this toy is to bring the elements into a predetermined regular arrangement, which can be predetermined, for example, by the color scheme.

Starting from this prior art, it is the object of the present invention to create an improved stereometric structure, in particular stereometric toys.

According to a first proposal, this object is achieved by the features of claim 1. At least one of the spatial forms into which the stereometric structure or stereometric toy can be brought is a regular body, the surfaces of which are each formed from a surface of a polyhedron, namely from an undivided surface of the polyhedron.

geöffneten Stellung

befindet, kann ein aus Polyedern gleicher Größe hergestelltes Gebilde, das sich in der Grundstellung befindet, durch das in der geöffneten Stellung befindliche Gebilde hindurchbewegt werden. Dies gilt zumindest im mathematischen Sinn, also für Stereometriegebilde, die aus Ecken, Kanten und Flächen mit mathematisch infinitesimal kleiner Ausdehnung hergestellt sind. Bei der praktischen Ausführung kann es dann aufgrund der Ausdehnung der Ecken, Kanten und Flächen sein, daß die beschriebene Hindurchbewegung nicht möglich ist.According to a further proposal, for which protection is claimed independently, the object on which the invention is based is achieved by the features of claim 2. At least one of the spatial shapes into which the structure can be brought is a regular body, namely a cube, the surfaces of which are each formed from a surface of several polyhedra. At least one surface of the regular body, ie the cube, is formed by polyhedron surfaces that belong to polyhedra that are not immediately adjacent in the polyhedron chain or in the polyhedron ring. At least one other of the spatial forms into which the structure can be brought is a ring through which a cube of the same size in the basic position can be moved. This further spatial shape can be called the open position. If the structure is in this

open position

is, a structure made of polyhedra of the same size, which is in the basic position, can be moved through the structure in the open position. This applies at least in the mathematical sense, i.e. for stereometric structures that are made up of corners, edges and surfaces with a mathematically infinitesimally small dimension. In the practical implementation it may then be due to the expansion of the corners, edges and surfaces that the described movement through is not possible.

According to a further proposal, for which protection is claimed independently, the object on which the invention is based is achieved by the features of claim 3. At least one of the spatial shapes into which the structure can be brought is a regular body, which is different from a cube and whose surfaces are each formed from a surface of several polyhedra.

The stereometric structures according to the invention can be divided into a first group, in which the surfaces of the regular body are undivided, and a second group, in which the surfaces of the regular body are divided. The solution according to claim 1 relates to the first group, the solution according to claims 2 and 3 the second group. The second group can in turn be divided into a first sub-group, in which the regular body is a cube, and in a second sub-group, which comprises regular bodies that are different from a cube. The first subgroup is the subject of claim 2, the second subgroup is the subject of claim 3.

A stereometric toy according to the proposals according to the invention stimulates the sense of form. It also trains the player's logic skills. It is also particularly appealing in appearance.

The chain or ring of articulated polyhedra is formed in such a way that the polyhedra represent a complete regular body in at least one of the spatial shapes that can be formed from them, which can be referred to as the "basic position". In this context, “complete” is to be understood to mean that all surfaces of the regular body are formed by surfaces of the polyhedra, it being possible for the surfaces of the regular body to be divided one or more times.

In this basic position, the stereometric toy according to the invention thus assumes a particularly appealing form, since the regular bodies convey a particularly beautiful appearance due to their high degree of regularity.

It is crucial that the basic position can be formed by a single closed arrangement, ie a chain or a ring of polyhedra. Therefore, no parts can be lost. Under a full regular body modifications of such are also to be understood. For example, the surfaces can be designed in relief rather than smooth or imperfect (for example with cut corners or with holes in the middle). Finally, the individual surfaces can also be formed by wire frames, so that a wire structure is formed overall.

Decisive for belonging to the invention is therefore the relationship of a design to the geometric shape and the sequence of certain connections of the polyhedra on which the design is based, but not the final design and the purpose which the designs are intended to fulfill (e.g. as an advertising medium, as a kit) , as lamp design).

In the present context, regular bodies are understood to mean all Platonic bodies and Archimedean bodies, as well as the rhombic dodecahedron and the rhombic thirty-surface. The edges of these bodies are all the same length.

Platonic bodies are known to be the tetrahedron, the cube, the octahedron, the icosahedron and the dodecahedron. Known examples of Archimedean bodies are the cube stump, the cuboctahedron, the octahedron stump, the dodecahedron stump, the icosidodecahedron, the icosahedron stump and tetrahedron stump (cf. for example the publication "Platonic and Archimedean Bodies, their Star Shapes and Polar Formations", Paul Adam / Arnold Wyss, Verlag Freies Geistesleben, 1984).

If the polyhedra are detached from the basic position of the regular body, a chain or ring that gives the impression of a high degree of irregularity generally arises, which does not suggest that they can be put together again to form a Platonic or Archimedean body. For this reverse Step, depending on the number of polyhedra, requires a high degree of skill, logical understanding and flexible thinking, so that these skills are promoted when playing with the stereometric toy according to the invention.

In summary, the stereometric toy according to the invention not only stimulates the sense of beautiful (geometric) shapes, but also involuntarily trains the agility of thinking in the player, whereby it particularly promotes judgment formation from the point of view. The appearance of the toy is appealing and remains interesting for a long time.

Advantageous further developments are described in the subclaims.

The polyhedra are preferably identical to one another and / or mirror-image identical. The polyhedra therefore each have the same or, in mirror image, the same shape. Similar to the kaleidocycles, in which a ring is formed from a multiplicity of tetrahedra, this regularity initially creates an aesthetically pleasing impression even outside the basic position. In addition, however, this also places higher demands on the logical skills for generating the basic position, since no reference can be made to different sizes or shapes. Finally, the uniformity of the large number of polyhedra also means that, in their basic position, they divide the regular body symmetrically, at least in terms of their external appearance, so that the confusion which promotes logic skills is further increased when the basic position is dissolved. The aesthetic appearance is particularly advantageous.

It is also advantageous if the polyhedra are articulated to one another at respective edges. It is also conceivable, for example, the connection at corners of the polyhedra, which would possibly increase the mobility and complexity of the toy. The connection at edges, however, has the advantages of particularly simple manufacture and handling and produces greater regularity in handling the toy.

According to a preferred embodiment, each polyhedron is connected to another polyhedron at two different edges. As a result, the desired chain structure or ring structure is achieved in a particularly simple manner. In individual cases, a polyhedron can also be connected to other polyhedra at three edges.

A further advantageous embodiment is characterized in that, in the basic position, all those connections of the polyhedra immediately adjacent in the polyhedron ring or in the polyhedron chain lie on edges of the regular body which connect such adjacent polyhedra which have surfaces which are in the basic position of the stereometric structure different areas of the regular body. In this way it can be achieved that the polyhedron ring can be turned into a hollow shape. At the same time, this describes the first necessary basic condition for all those forms that are to be completely reversible. The second basic requirement for such complete reversibility is that the stereometric structure must consist of at least twelve polyhedra. A third basic condition for complete reversibility is that the surfaces of the regular body must always be divided into at least two. The fulfillment of all three mentioned conditions is however no guarantee for an actual reversibility.

Another advantageous development is characterized in that the basic position is a cube and that at least twelve polyhedron connecting edges lie on edges of the cube. So the regular body is a platonic body, namely a cube that is formed from a polyhedron chain, in which at least twelve connections of the polyhedra come to rest in the basic position on the twelve cube edges. In contrast to this, in the known design according to GB-OS 2 108 395 the arrangement is such that only six polyhedron connections lie on cube edges.

According to a further preferred embodiment, the polyhedra partially fill the regular body in the basic position.

Another advantageous development is characterized in that a cavity in the form of a regular body is formed in the regular body.

According to a further preferred embodiment, the polyhedra completely fill the regular body in the basic position. In addition to the feature according to the invention that the surfaces of the regular body are completely formed by the polyhedra in the basic position, this gives the impression of a particularly compact toy, although it seems surprising that this compact arrangement of polyhedra from the regular basic position into one largely irregular structure can be resolved and vice versa. As a modification, it is possible to form a cavity inside the regular body, which in turn can be regular. This measure allows several toys according to the invention to be nested one inside the other. In addition, with appropriate cavity formation, a cube can be turned inside out into a pentagon dodecahedron.

Furthermore, it is particularly advantageous if a corner of each polyhedron lies in the center of the regular body. This usually results in the polyhedra being arranged in the basic position symmetrically with respect to the regular body. This means that the impression of symmetry and harmony in the basic position is further increased, which makes the discrepancy between the basic position and the irregularly appearing broken chain or ring shape appear even larger.

The polyhedra can be connected to form a ring. As a result, the compactness of the toy according to the invention is retained even in the state released from the basic position. It is also possible to connect the polyhedra to several rings that are connected to each other.

According to a further advantageous development, the ring can be turned inside out. By cleverly laying the connections between the polyhedra, it is possible to make the ring evertable. This means that the ring formed from the polyhedra can be rotated in the state released from the basic position. The ring can be partially or completely inverted. When completely reversible, the ring can be "rotated" by 360 °. It is particularly advantageous here that at least some of the realizable stereometric toys according to the invention can be "turned out" based on a certain inverted state. For example, a rhombic dodecahedron can be created from a cube, the edge lengths of which correspond to half the space diagonal of the cube. The basic position can usually only be restored from a certain rotational state. This increases the demands on the logical abilities of the player, and thus contributes to the fact that the toy - in this context, similar to the Rubik cube - remains interesting for a long time.

According to a preferred embodiment, the regular body is a cube with corners A, B, C, D, E, F, G, H and a center point O, the cube being formed by a chain or ring of polyhedra EFHO, BEFO, BFGO, FGHO, CHGO, CBGO, BCDO, CDHO, DAHO, ABDO, ABEO, AEHO, which are each connected via their edges EF, BF, FG, GH, CG, BC, CD, DH, AD, AB, AE, EH .

In the basic position, this embodiment of the stereometric structure or stereometric toy according to the invention is a cube, the side surfaces of which are divided diagonally and the polyhedron connections all lie on cube edges. The resulting polyhedron ring can be turned inside out. It is particularly interesting in this embodiment that a rhombic dodecahedron can be formed with the polyhedron ring by a complicated rotation process or, if there is a corresponding cavity formation in the interior of the cube, a pentagon dodecahedron can also be formed after its inversion, which is hollow on the inside. The cavity formed inside is cube-shaped with the same dimensions as the cube in the basic position. This embodiment can be transformed into a 24-polyhedral structure by introducing a division by the second cube side diagonal. The additional connecting edges all lie, for example, on the space diagonals going through the center O.

According to a further preferred embodiment, the regular body is an octahedron with corners A, B, C, D, E, F and a center O, the octahedron being formed by a chain or a ring of polyhedra ABCO, BCFO, BEFO, DEFO , CDFO, ACDO, ADEO, ABEO, which are each connected via their edges CO, BF, EO, DF, CO, AD, EO, AB.

This embodiment is particularly visually appealing since the surfaces of the octahedron are not subdivided in the basic position. However, the polyhedron ring is not completely invertible, so that the variability of this toy compared to the other embodiments of the invention remains.

According to a further preferred embodiment, the regular body is an octahedron with corners A, B, C, D, E, F and a center O, the edges BC, CD, ED, EB each having a center G, H, I, K. , and where the octahedron is formed is by a chain or ring of polyhedra ABGO, AGCO, GCFO, CHFO, ACHO, AHDO, DFHO, EFKO, AEKO, AEIO, EFIO, DFIO, ADIO, ABKO, BFKO, BFGO, which are each connected via their edges AO , GC, OF, CH, AO, HD, OF, DI, AO, EI, FO, KE, AO, BK, FO, BG. Alternatively, the edge connections AO, GC, FC, CH, AO, HD, FD, DI, AO, EI, FE, KE, AO, BK, BF, BG can be formed, so that the octahedron can be turned inside out.

With their 16 polyhedra, these embodiments already have a confusing variety of play options as soon as you leave the basic position. Also, restoring the basic position for an inexperienced player is not easy to accomplish.

According to a further preferred embodiment, the regular body is a tetrahedron with corners A, B, C, D and a center O, the surfaces ABC, ACD, BCD, ABD having a respective center E, F, G, H, and wherein the Tetrahedron is formed by a chain or ring of polyhedra BAEO, BECO, AECO, ACFO, CFDO, DFAO, CGDO, CGBO, DGBO, DHBO, BHAO, AHDO, which are each connected via their edges CO, AO, AD, DO , BO, AB, AO, CO, CB, BO, DO, DC.

The polyhedron ring is half turnable, whereby the twelve polyhedra can be handled with considerable variability. By a further regular division of the tetrahedron surfaces, for example by dividing the polyhedra described, a further reversibility can also be achieved here. The described polyhedron ring itself can be turned inside out as a basis for such designs, although the 12 polyhedra can nevertheless be handled with considerable variability. It goes without saying that polyhedron rings which result from a further division of the tetrahedral surface do not therefore leave the scope of the invention.

According to a further preferred embodiment, the regular body is a tetrahedron with corners A, B, C, D and a center O, the edges AB, AC, AD, BC, CD, DB each having a center O _x , N, M, I , K, L and where the surfaces ABC, ACD, BCD, ABD each have a center E, F, G, H, and wherein the tetrahedron is formed by a chain or a ring of polyhedra BIO _x EO, CNIEO, AO _x NEO, ANMFO, CNKFO, DKMFO, BILGO, CIKGO, DKLGO, AO _x MHO, BO _x LHO, DLMHO, which are each connected via their edges AN, MO, KO, CK, IO, LO, LD, MO, O _x O, BO _x , IO, NO.

This embodiment is also visually particularly appealing in its basic position. The ring can be turned inside out. There is an amazing variability in the polyhedron ring. It is unexpectedly difficult to return to the basic position.

According to a further preferred embodiment, the regular body is a dodecahedron which is formed by a chain or a ring of twelve polyhedra, which are each formed by one of the twelve pentagons on the surface of the dodecahedron and by the connection of the corners of this pentagon to the center O of the dodecahedron formed surfaces, and wherein the polyhedra are each connected via side edges of their pentagonal surfaces.

It is preferable if the corners AI, KN, O _x , PU of the dodecahedron pentagons BKLME, MEFNS, NSUTO _x , NO _x GCF, FCABE, ACGHD, HGPTO _x , PHDIQ, DIKBA, IKLRQ, QRUTP, RUSML on its surface describe, which are each connected via their edges ME, SN, NO _x , FC, AC, HG, PH, DI, IK, QR, RU, LM.

According to an alternative preferred embodiment, the corners describe AI, KN, O _x , PU of the dodecahedron pentagons BEMLK, BEFCA, BADIK, KIQRL, QRUTP, QPHDI, PHGO _x T, HGCAD, GCFNO _x , O _x NSUT, SURLM, SMEFN on its surface , which are connected by their edges BE, BA, KI, QR, QP, PH, HG, GC, O _x N, SU, SM, ME.

The two alternative embodiments of the dodecahedron describe alternative concatenations of the same polygon types from which the dodecahedron is formed. All connecting edges of the polyhedra thus lie on the surface of the dodecahedron. In principle, there can also be other polyhedron rings with other edge connections (e.g. a dodecahedron polyhedron ring with the edges DJ, AB, FC, CG, GH, TO _x , NS, ME, KL, RL, RU, PQ) that are movable and possibly can be turned inside out. The alternative chaining variants described above, however, show a certain regularity and are therefore particularly preferred.

In a further preferred embodiment, the regular body is a dodecahedron with corners AI, KN, O _x , PU, which delimit twelve pentagons on its surface, the edges KI, HG, EF, LM, PQ, NO _x centers a, b, have c, d, e, f, the dodecahedron being formed by a chain or ring of twenty-four polyhedra, each formed by half of one of the pentagons, the bisecting line being formed by the edge centers af and the opposite corner of the Pentagon runs, and through the surfaces formed by the connection of the corners of this pentagon half with the center O of the dodecahedron.

The twenty-four polyhedra are preferably connected via their edges Ac, cF, FN, Nf, Uf, O _x f, O _x G, Gb, Ab, Hb, HP, Pe, Ue, Qe, Ql, Ia, Aa, Ka, KL, Ld, Ud, Md, ME, Ec.

Alternatively, the twenty-four polyhedra are connected by their edges AO, Fc, FN, Nf, UO, O _x f, O _x G, Gb, AO, Hb, HP, Pe, UO, Qe, Ql, Ia, AO, Ka , KL, Ld, UO, Md, ME, Ec.

The two alternative preferred embodiments of this type of dodecahedron toy are both reversible. In the first alternative, a spatially narrower reversible ring is created, which demands greater skill and greater spatial understanding from the player. The second alternative results in a longer ring that is easier to handle. Here it is easier to find new spatial arrangements.

In general, these two dodecahedron variants are already relatively complex, since a total of twenty-four polyhedra require a high degree of logical understanding and intellectual mobility in order to return from the "disordered" state to the basic position.

According to a further preferred embodiment, the regular body is a rhombic dodecahedron with corners AI, KN, O _x , which is formed by a ring of twelve polyhedra, each formed by one of the twelve rhombuses on the surface of the rhombic dodecahedron and by the connection of the Corners of these rhombi with the center O of the rhombic dodecahedron formed surfaces.

The polyhedra are preferably connected via their edges FO, FL, CG, GO, GM, DH, HO, HN, EI, IO, IK, BF.

Alternatively, it is preferred to connect the polyhedra via their edges EB, HI, IK, BF, FC, KL, LM, GC, DG, NM, HN, ED.

Although the rhombic dodecahedron is neither an Archimedean nor a Platonic body, it is nevertheless a regular body in the sense of the invention. The edges are all the same length. This creates a visual impression of great regularity.

The ring structures are largely regular in both cases. The first alternative is a ring structure around a point with four-fold symmetry, the second alternative is a ring structure around a point with three-fold symmetry.

In a further preferred embodiment, the regular body is an icosahedron with corners AI, KM, which delimit twenty triangles on its surface, the edges BC, CD, DE, EF, FB, GH, HI, IK, KL each having center points B ', C ', D', E ', F', G ', H', I ', K', L ', where the icosahedron is formed by forty polygons, each of which is formed by half of one of them the surface of the icosahedron and the triangles formed by the connection of the corners of the triangle half to the center O of the icosahedron, the icosahedron being formed by a chain or ring of polyhedra ACC'O, AC'DO, ADD'O, AD'EO, AEE'O, AE'FO, AFF'O, AF'BO, ABB'O, AB'CO, GBB'O, GB'CO, CGG'O, CG'HO, HCC'O, HC ' DO, DHH'O, DH'IO, IDD'O, ID'EO, EII'O, EI'KO, KEE'O, KE'FO, FKK'O, FK'LO, LFF'O, LF'BO, BLL'O, BL'GO, MGG'O, MG'HO, MHH'O, MH'IO, MII'O, MI'KO, MKK'O, MK'LO, MLL'O, ML'GO.

The forty polyhedra are preferably connected via their edges AO, C'D, DH, HH ', MO, H'I, ID, DD', AO, D'E, EI, II ', MO, I'K, KE , EE ', AO, E'F, FK, KK', MO, K'L, LF, FF ', AO, F'B, BL, LL', MO, L'G, GB, BB ', AO, B'C, CG, GG ', MO, G'H, HC, CC'.

Alternatively, the forty polyhedra are connected by their edges AC ', C'D, DH, HH', MH ', H'I, ID, DD', AD ', D'E, EI, II', MI ', I'K, KE, EE ', AE', E'F, FK, KK ', MK', K'L, LF, FF ', AF', F'B, BL, LL ', ML', L ' G, GB, BB ', AB', B'C, CG, GG ', MG', G'H, HC, CC '.

It goes without saying that the features mentioned above and those yet to be explained below can be used not only in the combination indicated in each case, but also in other combinations or on their own without departing from the scope of the present invention. Furthermore, it goes without saying that polyhedron rings which result from a further division of the regular surfaces of the Platonic solids do not therefore leave the scope of the invention.

The invention further relates to a polyhedron construction kit with a multiplicity of polyhedra or parts of such polyhedra which can be combined to form individual polyhedra and hinge elements which is characterized in accordance with the invention in that one or more stereometric structures or stereometric toys according to the invention can be produced with it.

Further exemplary embodiments result from the drawing and are explained in more detail in the following description.

Fig. 1

eine erste Ausführungsform des erfindungsgemäßen Stereometriespielzeuges mit der Grundstelleung eines Würfels;

Fig. 2

eine zweite Ausführungsform des erfindungsgemäßen Stereometriespielzeuges mit der Grundstellung eines Oktaeders;

Fig. 3

eine dritte Ausführungsform des erfindungsgemäßen Stereometriespielzeuges mit der Grundstellung eines Oktaeders, jedoch mit einer anderen Anzahl von Polyedern als der Oktaeder von Fig. 2;

Fig. 4

eine vierte Ausführungsform des erfindungsgemäßen Stereometriespielzeuges mit der Grundstellung eines Tetraeders;

Fig. 5

eine fünfte Ausführungsform des erfindungsgemäßen Stereometriespielzeuges mit der Grundstellung eines Tetraeders, jedoch mit einer anderen Raumaufteilung als der Tetraeder von Fig. 4;

Fig. 6

eine sechste Ausführungsform des erfindungsgemäßen Stereometriespielzeuges mit der Grundstellung eines Dodekaeders;

Fig. 7

eine siebte Ausführungsform des erfindungsgemäßen Stereometriespielzeuges mit der Grundstellung eines Dodekaeders, jedoch mit einer alternativen Verbindung der das Dodekaeder bildenden Polyeder;

Fig. 8

eine Draufsicht auf eine Abwicklung der das Dodekaeder von Fig. 7 bildenden Polyederkette;

Fig. 9

eine achte Ausführungsform des erfindungsgemäßen Stereometriespielzeuges mit der Grundstellung eines Dodekaeders, jedoch mit einer anderen Raumaufteilung als die Dodekaeder der Fig. 6 bis 8;

Fig. 10

eine neunte Ausführungsform des erfindungsgemäßen Stereometriespielzeuges mit der Grundstellung eines Dodekaeders und derselben Raumaufteilung wie das Dodekaeder von Fig. 9 und mit derselben Polyederverkettung, gezeigt aus einer anderen Perspektive;

Fig. 11

eine zehnte Ausführungsform des erfindungsgemäßen Stereometriespielzeuges mit der Grundstellung eines Rhombendodekaeders;

Fig. 12

eine elfte Ausführungsform des erfindungsgemäßen Stereometriespielzeuges mit der Grundstellung eines Rhombendoedekaeders, jedoch mit einer anderen Polyederverkettung als der Rhombendodekaeder von Fig. 11;

Fig. 13

eine zwölfte Ausführungsform des erfindungsgemäßen Stereometriespielzeuges mit der Grundstellung eines Ikosaeders;

Fig. 14

eine Seitenansicht einer dreizehnten Ausführungsform des erfindungsgemäßen Stereometriespielzeuges mit der Grundstellung eines Ikosaeders, jedoch mit einer anderen Raumaufteilung als das Ikosaeder von Fig. 13;

Fig. 15

eine Draufsicht auf das Ikosaeder von Fig. 14;

Fig. 16

eine vierzehnte Ausführungsform des erfindungsgemäßen Stereometriespielzeugs mit der Grundstellung eines Oktaeders;

Fig. 17

eine fünfzehnte Ausführungsform mit der Grundstellung eines Oktaeders, jedoch mit einer anderen Flächenteilung als bei dem Oktaeder gemäß Fig. 16;

Fig. 18

eine sechszehnte Ausführungsform mit der Grundstellung eines Tetraeders und

Fig. 19

eine siebzehnte Ausführungsform mit der Grundstellung eines Würfels.

Show it:

Fig. 1

a first embodiment of the stereometric toy according to the invention with the basic position of a cube;

Fig. 2

a second embodiment of the stereometric toy according to the invention with the basic position of an octahedron;

Fig. 3

a third embodiment of the stereometric toy according to the invention with the basic position of an octahedron, but with a different number of polyhedra than the octahedron of Fig. 2;

Fig. 4

a fourth embodiment of the stereometric toy according to the invention with the basic position of a tetrahedron;

Fig. 5

a fifth embodiment of the stereometric toy according to the invention with the basic position of a tetrahedron, but with a different room layout than the tetrahedron of Fig. 4;

Fig. 6

a sixth embodiment of the stereometric toy according to the invention with the basic position of a dodecahedron;

Fig. 7

a seventh embodiment of the stereometric toy according to the invention with the basic position of a dodecahedron, but with an alternative connection of the polyhedra forming the dodecahedron;

Fig. 8

a plan view of a development of the polyhedron chain forming the dodecahedron of FIG. 7;

Fig. 9

an eighth embodiment of the stereometric toy according to the invention with the basic position of a dodecahedron, but with a different room layout than the dodecahedron of FIGS. 6 to 8;

Fig. 10

a ninth embodiment of the stereometric toy according to the invention with the basic position of a dodecahedron and the same room layout as the dodecahedron of FIG. 9 and with the same polyhedron chaining, shown from a different perspective;

Fig. 11

a tenth embodiment of the stereometric toy according to the invention with the basic position of a rhombic dodecahedron;

Fig. 12

an eleventh embodiment of the stereometric toy according to the invention with the basic position of a rhombic dodecahedron, but with a different polyhedron chain than the rhombic dodecahedron of FIG. 11;

Fig. 13

a twelfth embodiment of the stereometric toy according to the invention with the basic position of an icosahedron;

Fig. 14

a side view of a thirteenth embodiment of the stereometric toy according to the invention with the basic position of an icosahedron, but with a different room layout than the icosahedron of Fig. 13;

Fig. 15

a plan view of the icosahedron of Fig. 14;

Fig. 16

a fourteenth embodiment of the stereometric toy according to the invention with the basic position of an octahedron;

Fig. 17

a fifteenth embodiment with the basic position of an octahedron, but with a different surface division than in the octahedron according to FIG. 16;

Fig. 18

a sixteenth embodiment with the basic position of a tetrahedron and

Fig. 19

a seventeenth embodiment with the basic position of a cube.

In Fig. 1 , a first embodiment of the stereometric toy according to the invention with the basic position of a cube is generally designated 10.

The cube 10 has corners A, B, C, D, E, F, G, H and a center O. The cube is formed by a ring of polyhedra EFHO, BEFO, BFGO, FGHO, CHGO, CBGO, BCDO, CDHO, DAHO, ABDO, ABEO, AEHO, of which the polyhedron BCDO is represented by hatching its sides. The polyhedra are connected to form a ring by their edges EF, BF, FG, GH, CG, BC, CD, DH, AD, AB, AE, EH.

2 shows a second embodiment of the stereometric toy according to the invention with the basic position of an octahedron 12. The octahedron 12 has corners A, B, C, D, E, F and a center O. The octahedron is formed by a ring of polyhedra ABCO, BCFO , BEFO, DEFO, CDFO, ACDO, ADEO, ABEO, which are each connected via their edges CO, BF, EO, DF, CO, AD, EO, AB. The polyhedron BCFO is shown in Fig. 2 by hatching its sides.

3 shows a third embodiment of the stereometric toy according to the invention with the basic position of an octahedron 14. The octahedron has corners A, B, C, D, E, F and a center O. The edges BC, CD, ED, EB of the octahedron each have a center G, H, I, K. The octahedron is formed by a ring of polyhedra ABGO, AGCO, GCFO, CHFO, ACHO, AHDO, DFHO, EFKO, AEKO, AEIO, EFIO, DFIO, ADIO, ABKO, BFKO, BFGO . The polyhedra are each connected via their edges AO, GC, OF, CH, AO, HD, OF, DI, AO, EI, FO, KE, AO, BK, FO, BG. The polyhedron GCFO is shown in Fig. 3 by hatching its sides.

4 shows a fourth embodiment of the stereometric toy according to the invention with the basic position of a tetrahedron 16. The tetrahedron has corners A, B, C, D and a center O. The edges AB, AC, AD, BC, CD, DB each have a center O _x , N, M, I, K, L. The areas ABC, ACD, BCD, ABD each have one Center E, F, G, H. The tetrahedron is formed by a ring of polyhedra BIO _x EO, CNIEO, AO _x NEO, ANMFO, CNKFO, DKMFO, BILCO, CIKGO, DKLGO, AO _x MHO, BO _x LHO, DLMHO. The polyhedra are each connected via their edges AN, MO, KO, CK, IO, LO, LD, MO, O _x O, BO _x , IO, NO.

5 shows a fifth embodiment of the stereometric toy according to the invention with the basic position of a tetrahedron 18. The tetrahedron has corners A, B, C, D and a center O. The surfaces ABC, ACD, BCD, ABD each have a center E, F, G, H. The tetrahedron is formed by a ring of polyhedra BAEO, BECO, AECO, ACFO, CFDO, DFAO, CGDO, CGBO, DGBO, DHBO, BHAO, AHDO. The polyhedra are each connected via their edges CO, AO, AD, DO, BO, AB, AO, CO, CB, BO, DO, DC. The polyhedron ABEO is shown in Fig. 5 by hatching its sides.

6 shows a sixth embodiment of the stereometric toy according to the invention with the basic position of a dodecahedron 20. The dodecahedron 20 has corners AI, KN, O _x , PU, the pentagons BKLME, MEFNS, NSUTO _x , NO _x GCF, FCABE, ACGHD, HGPTO _x , PHDIQ, DIKBA, IKLRQ, QRUTP, RUSML on its surface. The dodecahedron 20 is formed by a ring of twelve polyhedra. Each polyhedron is formed by one of the twelve pentagons on the surface of the dodecahedron 20 and the surfaces formed by connecting the corners of the pentagon to the center O of the dodecahedron 20. The polyhedra are connected via the side edges of their pentagonal surfaces, specifically via the edges ME, SN, NO _x , FC, AC, HG, PH, DI, IK, QR, RU, LM.

A seventh embodiment of the stereometric toy according to the invention with the basic position of a dodecahedron is generally designated by the reference number 22 in FIG. 7 . The dodecahedron 22 has corners AI, KN, O _x , PU, the pentagons BEMLK, BEFCA, BADIK, KIQRL, QRUTP, QPHDI, PHGO _x T, HGCAD, GCFNO _x , O _x NSUT, Describe SURLM, SMEFN on its surface. The dodecahedron is formed by a ring of twelve polyhedra. Each polyhedron is formed by one of the twelve pentagons on the surface of the dodecahedron 22 and the surfaces formed by connecting the corners of this pentagon to the center O of the dodecahedron 22. The polyhedra are connected via the edges BE, BA, KI, QR, QP, PH, HG, GC, O _x N, SU, SM, ME. A development of the polyhedron of the polyhedron chain thus formed is shown in plan view in FIG. 8 . The polyhedra 1 and 12 in FIG. 8 are connected to one another at the edges provided with arrows.

An eighth embodiment of the stereometric toy according to the invention with the basic position of a dodecahedron 24 is shown in FIG. 9 . The dodecahedron 24 has corners AI, KN, O _x , PU, which delimit twelve pentagons on its surface. The edges KI, HG, EF, LM, PQ, NO _x have centers a, b, c, d, e, f. The dodecahedron 24 is formed by a ring of twenty-four polyhedra. Each polyhedron is formed by half of one of the pentagons, the halving line running through the center points af and the opposite corner of the pentagon, and through the surfaces formed by connecting the corners of this pentagon half to the center O of the dodecahedron 24. The twenty-four polyhedra are connected by their edges Ac, cF, FN, Nf, Uf, O _x f, O _x G, Gb, Ab, Hb, HP, Pe, Ue, Qe, Ql, Ia, Aa, Ka, KL, Ld, Ud, Md, ME, Ec.

FIG. 10 shows a ninth embodiment of the stereometric toy according to the invention with the basic shape of a dodecahedron 26. The dodecahedron 26 is divided into the same 24 polyhedra as the dodecahedron 24 from FIG. 9. However, the connection of the polyhedra to one another is different, namely via the edges AO , Fc, FN, Nf, UO, O _x f, O _x G, Gb, AO, Hb, HP, Pe, UO, Qe, Ql, Ia, AO, Ka, KL, Ld, UO, Md, ME, Ec .

Fig. 11 shows a tenth embodiment of the stereometric toy according to the invention with the basic shape of a rhombic dodecahedron 28. The rhombic dodecahedron 28 has corners AI, KN, O _x . The rhombic dodecahedron is divided into twelve polyhedra. Each polyhedron is formed by one of the twelve rhombuses on the surface of the rhombic dodecahedron 28 and the surfaces formed by connecting the corners of this rhombus to the center O of the rhombic dodecahedron 28. The polyhedra are connected to form a ring via their edges FO, FL, CG, GO, GM, DH, HO, HN, EI, IO, IK, BF.

12 shows an eleventh embodiment of the stereometric toy according to the invention with the basic position of a rhombic dodecahedron 30. The rhombic dodecahedron 30 is divided into the same polyhedra as the rhombic dodecahedron 29 from FIG. 11. However, the polyhedra are connected differently to form a ring, namely via their edges EB , HI, IK, BF, FC, KL, LM, GC, DG, NM, HN, ED.

13 shows a twelfth embodiment of the stereometric toy according to the invention with the basic position of an icosahedron 32 as a development in plan view. The polyhedra forming the icosahedron are each formed by one of the twenty triangles on the surface of the icosahedron and by the surfaces formed by connecting the corners of the respective triangle to the center O of the icosahedron. The edge connections of the polyhedra of this icosahedron are all on the surface, so that the spatial structure can be characterized solely by the development shown in FIG. 13. The process can be put together to form a ring.

A thirteenth embodiment of the stereometric toy according to the invention with the basic position of an icosahedron is generally designated by 34 in FIGS. 14 and 15 . The icosahedron has corners AI, KM. The edges BC, CD, DE, EF, FB, GH, HI, IK, KL each have center points B ', C', D ', E', F ', G', H ', I', K ', L '. The icosahedron 34 is formed by forty polyhedra, each formed by half of one of the triangles located on the surface of the icosahedron and by the surfaces created by connecting the corners of the triangle half to the center O of the icosahedron. The triangles on the surface of the icosahedron are each divided so that the bisection line runs through the points B 'to L' and through the opposite corner of the respective triangle. The icosahedron 34 is thus formed by a chain of polyhedra ACC'O, AC'DO, ADD'O, AD'EO, AEE'O, AE'FO, AFF'O, AF'BO, ABB'O, AB'CO , GBB'O, GB'CO, CGG'O, CG'HO, HCC'O, HC'DO, DHH'O, DH'IO, IDD'O, ID'EO, EII'O, EI'KO, KEE 'O, KE'FO, FKK'O, FK'LO, LFF'O, LF'BO, BLL'O, BL'GO, MGG'O, MG'HO, MHH'O, MH'IO, MII'O , MI'KO, MKK'O, MK'LO, MLL'O, ML'GO.

There are generally two particularly regular versions of connecting these polyhedra into a chain. In the first alternative, the connecting edges are AO, C'D, DH, HH ', MO, H'I, ID, DD', AO, D'E, EI, II ', MO, I'K, KE, EE' , AO, E'F, FK, KK ', MO, K'L, LF, FF', AO, F'B, BL, LL ', MO, L'G, GB, BB', AO, B'C , CG, GG ', MO, G'H, HC, CC'. This creates a longer polyhedron ring. The connecting edges also lie inside the icosahedron 34.

In the second alternative, the polyhedra described above are connected via the following connecting edges: AC ', C'D, DH, HH', MH ', H'I, ID, DD', AD ', D'E, EI, II' , MI ', I'K, KE, EE', AE ', E'F, FK, KK', MK ', K'L, LF, FF', AF ', F'B, BL, LL', ML ', L'G, GB, BB', AB ', B'C, CG, GG', MG ', G'H, HC, CC'. The resulting polyhedron ring is shorter and more complicated to change. All connecting edges are on the surface of the icosahedron.

16 shows a fourteenth embodiment with the basic position of an octahedron which is formed by eight triangles. Every triangle has a center. The octahedron is formed by twenty-four polyhedra, each of which is formed is by a partial triangle of each triangle of the octahedron and the surfaces created by connecting the corners of the partial triangle to the center of the octahedron. Each partial triangle is formed by two corner points of an octahedron triangle and the center of the octahedron triangle.

17 shows a fifteenth embodiment with the basic position of an octahedron. 16, each triangle of the octahedron has a center. In contrast to the embodiment according to FIG. 16, however, the partial quadrilaterals of an octahedron triangle are not formed by lines which run from the center of the octahedron triangle to a corner point of the octahedron triangle, but by lines which run from the center of the The octahedron triangle runs to the center of an edge connecting two corners of the octahedron triangle. In the embodiment according to FIG. 17, the octahedron is formed by twenty-four polyhedra, each of which is formed by a partial quadrilateral located on the surface of the octahedron and the surfaces resulting from the connection of the corners of the partial quadrilateral to the center of the octahedron. Each partial quadrilateral consists of the center of an octahedron triangle, a corner of the octahedron triangle and the two centers of the edges of the octahedron, which run away from the said corner of the octahedron.

18 shows a sixteenth embodiment with the basic position of a tetrahedron with the corners A, B, D, E and the edges AB, AD, AE, BD, DE, EB. The edges AE and BD have centers F and C. The tetrahedron is formed by eight polyhedra, each of which is formed by half of one of the triangles located on the surface of the tetrahedron and by the connection of the corners of the triangle half to the Center O of the tetrahedron resulting areas. The triangles on the surface of the tetrahedron are each divided so that the halving line runs from the edge centers C and F to the opposite corner A and E as well as B and D. The tetrahedron is with it formed by a chain of polyhedra ABCO, BCEO, BEFO, FEDO, EDCO, CDAO, AFDO, AFBO. The polyhedra are connected at the edges BC, BE, EF, ED, CD, AD, AF, AB. The tetrahedron is movable, but cannot be turned inside out. However, it can be turned into half a cube.

19 shows a seventeenth embodiment with the basic position of a cube with the corners A, L, Q, C, D, I, W, F. The edges AL, LQ, QC, CA, AD, LI, QW, CF, DI, IW, WF, FD have center points M, P, R, B, N, K, U, 2, H, V, Y, E. The cube surfaces ALQC, ADIL, LIWQ, QWFC, CFDA, DIWF have center points S, O, T, Z, G, X. The center of the cube is labeled 1. The cube is formed by a ring of eight polyhedra, which in turn are cubes (partial cubes). Each sub-cube is formed by the sub-squares on the surface of the cube, which adjoin a cube corner, and by squares, which are each formed from the center of the edge starting from the cube corner, the center points of two of the cube corner comprehensive cube surfaces and the cube center 1. The cube is thus formed by a chain of polyhedra MSBAGNO1, SBCRG2Z1, ONGEDHX1, G2ZEFYX1, MSPLOKT1, OKTHIVX1, OKTXHIY1, XVWYG2Z1. These polyhedra are connected at the edges SB, G2, XY, TU, PS, KT, HX, NG. 19 can be brought into a ring position, which allows a cube of the same size in the basic position to be moved through the ring.

The above-described embodiments of the stereometric toy according to the invention can be made from a wide variety of materials, for example from cardboard or plastic. The surfaces can be smooth or relief-like and painted with different colors. It is also conceivable to provide the polygons with fluorescent colors or to design the surfaces graphically or holographically. Furthermore, it is conceivable to design the individual polyhedra as frame models made of plastic or metal. The polyhedron surfaces can be made of transparent plastic (plexiglass), it being conceivable to incorporate bulbs into the polyhedron. To increase complexity, the integration of reflective surfaces is possible.

In the simplest case, the edge connections can be formed by film hinges. However, hinges made of fabric tape or the like are also conceivable.

Finally, regardless of the application to the stereometric toy according to the invention, it is generally possible to provide a polyhedron construction kit with a multiplicity of polyhedra or parts which can be assembled to form such polyhedra and which can be connected to one another at their edges by hinge elements. The hinge elements are also part of the polyhedron modular system and are each equipped with connecting means for coupling to an edge of two polyhedra. The polyhedra of the modular system are provided with appropriate connecting means at their edges. Ideally, the connecting means are snap-in connections so that the hinges can be releasably connected to the edges. Although it is generally conceivable to provide the connecting means on the polyhedra on the polyhedron surfaces, it is preferred to “let” the connecting means into the polyhedron surfaces so that the external appearance and the functionality are not disturbed.

The polyhedron construction kit preferably contains all of the polyhedra of one embodiment or the polyhedra of several of the above-described embodiments. In the latter case, it is advantageous if the edge lengths of the different polyhedra are matched to one another in such a way that the polyhedra of the different embodiments can also be connected to one another.

As already described above, instead of completely filling the respective regular bodies in the basic position, it is also possible to have one inside each Provide cavity that has the shape of a regular body, for example. A further stereometric toy according to the invention can then be inserted into this cavity so that the stereometric toys can be nested one inside the other, or a cube can be turned inside out into a pentagon dodecahedron.

Stereometric structures according to the invention can be found by a step-by-step procedure. In a first step, the polyhedra are determined by simple symmetrical structuring of the regular body, including the center of the regular body. In the second step, the most regular chain formations that open to form a polyhedron ring are sought and then their modifications - by connecting the polyhedra at the respective edges - are examined with the aim of creating a structure that can move in space. In the ideal state, the ring found can be turned into a hollow shape. In the third step, known shapes can be excluded.

This procedure is explained below using the example of the tetrahedron with reference to FIG. 20. The simplest tetrahedron structure is determined in the first step. The center point and the tetrahedron vertices divide the tetrahedron into four parts with undivided surfaces (FIG. 20a). In this structure, a possible polyhedral ring cannot be turned inside out (second step).

Mitsubishi

). Sie kann auch als mittelpunktsymmetrische Gliederung der Dreiecksfläche aufgefaßt werden. Durch eine weitere Untergliederung der Dreiecksfläche erhält man sechsteilige Dreiecksflächen (Fig. 20f).So you have to further divide the regular triangular surfaces of the tetrahedron (another first step). It is possible, for example, to divide the regular tetrahedron triangle into two or three parts according to the symmetry relationships (FIGS. 20b, 20c, 20d). An interesting further modification is the structure shown in Fig. 20e (similar to the logo of

Mitsubishi

). It can also be interpreted as a symmetrical structure of the triangular surface. By a further subdivision of the triangular surface gives six-part triangular surfaces (Fig. 20f).

All these divisions of the tetrahedron surfaces, including the center of the tetrahedron, result in a tetrahedron consisting of eight (FIG. 20b), twelve (FIGS. 20c-e) or twenty-four (FIG. 20f) polyhedra.

The just described can be transferred to the octahedron. The eight-link polyhedron chain (first step) is the only possible polyhedron chain that opens and moves in space (second step) with undivided octahedral surface. It is partially reversible. It is shown in Fig. 20g.

If you look at the cube, the simplest division of space (through the center of the cube and the cube corners) is a six-link polyhedral structure (first step), which allows regular chain formation (second step), but is not movable in space. Only dividing the cube surfaces by a corresponding diagonal (first step) enables the formation of a twelve-link polyhedron chain that can move in space (second step). The most regular form of chain formation is when all the connections between the polyhedra lie on cube edges. A further division of this polyhedron chain by the second square diagonal (from twelve thus twenty-four polyhedra) is shown in FIG. 20. 20h shows an eight-part cube.

It goes without saying that stereometric structures which result from a less regular division of the surfaces of the regular body do not for this reason alone depart from the scope of the invention. For example, a division of the tetrahedral surface as in FIG. 20f and a stereometric structure resulting therefrom are within the scope of the invention.

Claims (38)

Stereometric images, in particular stereometric toys, consisting of a chain of polyhedra that can be closed or closed to form a ring,
wherein the structure can be brought into several different spatial forms and wherein at least one of these spatial shapes (basic position) is a regular body, the surfaces of which are each formed from a surface of a polyhedron. Stereometric structures, in particular stereometric toys, consisting of a chain of polyhedra that can be closed or closed to form a ring,
wherein the structure can be brought into several different spatial forms and wherein at least one of these spatial shapes (basic position) is a regular body, namely a cube, the surfaces of which are formed from a surface of several polyhedra,
characterized, that at least one surface of the cube is formed by polyhedron surfaces that belong to polyhedra that are not immediately adjacent in the polyhedron chain or ring, and that at least one other of the spatial shapes (open position) into which the structure can be brought is a ring through which a cube in the basic position can be moved. Stereometric structures, in particular stereometric toys, consisting of a chain of polyhedra that can be closed or closed to form a ring,
wherein the structure can be brought into several different spatial forms and wherein at least one of these spatial shapes (basic position) is a regular body, which is different from a cube and whose surfaces are each formed from a surface of several polyhedra. Stereometric structure according to one of the preceding claims, characterized in that the polyhedra are identical to one another and / or mirror-image identical. Stereometric structure according to one of the preceding claims, characterized in that the polyhedra are articulated to one another at respective edges. Stereometric structure according to claim 5, characterized in that each polyhedron is articulated at two different edges with a further polyhedron. Stereometric structure according to one of the preceding claims, characterized in that in the basic position all those connections of the polyhedra immediately adjacent in the polyhedron ring or in the polyhedron chain lie on edges of the regular body which connect such adjacent polyhedra which have surfaces which in the basic position of the Stereometric image lie on different surfaces of the regular body. Stereometric structure according to one of the preceding claims, characterized in that the basic position is a cube and that at least twelve polyhedron connecting edges lie on edges of the cube. Stereometric structure according to one of the preceding claims, characterized in that the polyhedra partially fill the regular body in the basic position. Stereometric structure according to claim 9, characterized in that a cavity in the form of a regular body is formed in the regular body. Stereometric structure according to one of claims 1 to 8, characterized in that the polyhedra completely fill the regular body in the basic position. Stereometric structure according to one of the preceding claims, characterized in that a corner of each polyhedron lies in the center of the regular body (12 to 30). Stereometric structure according to one of the preceding claims, characterized in that the polyhedra are connected to at least one ring, preferably to a plurality of rings connected to one another. Stereometric structure according to claim 13, characterized in that the ring can be turned inside out. Stereometric structure according to one of claims 2 and 4 to 14, characterized in that the regular body is a cube (10) with corners A, B, C, D, E, F, G, H and a center O and that the cube can be formed is connected by a chain or ring of polyhedra EFHO, BEFO, BFGO, FGHO, CHGO, CBGO, BCDO, CDHO, DAHO, ABDO, ABEO, AEHO, which are each connected via their edges EF, BF, FG, GH, CG , BC, CD, DH, AD, AB, AE, EH (Fig. 1). Stereometric structure according to one of claims 1 and 4 to 14, characterized in that the regular body is an octahedron (12) with corners A, B, C, D, E, F and a center O and that the octahedron is formed by a chain or a ring of polyhedra ABCO, BCFO, BEFO, DEFO, CDFO, ACDO, ADEO, ABEO, which are each connected via their edges CO, BF, EO, DF, CO, AD, EO, AB (Fig. 2). Stereometric structure according to one of claims 3 to 14, characterized in that the regular body is an octahedron (14) with corners A, B, C, D, E, F and a center O, the edges BC, CD, ED, EB each have a center G, H, I, K, and that the octahedron is formed by a chain or a ring of polyhedra ABGO, AGCO, GCFO, CHFO, ACHO, AHDO, DFHO, EFKO, AEKO, AEIO, EFIO, DFIO , ADIO, ABKO, BFKO, BFGO, which are each connected via their edges AO, GC, OF, CH, AO, HD, OF, DI, AO, EI, FO, KE, AO, BK, FO, BG or their edges AO, GC, FC, CH, AO, HD, FD, DI, AO, EI, FE, KE, AO, BK, BF, BG ( Fig. 3). Stereometric structure according to one of Claims 3 to 14, characterized in that the regular body is a tetrahedron (18) with corners A, B, C, D and a center O, the surfaces ABC, ACD, BCD, ABD being a respective center E , F, G, H, and that the tetrahedron is formed by a chain or ring of polyhedra BAEO, BECO, AECO, ACFO, CFDO, DFAO, CGDO, CGBO, DGBO, DHBO, BHAO, AHDO, each connected are over their edges CO, AO, AD, DO, BO, AB, AO, CO, CB, BO, DO, DC (Fig. 5). Stereometric structure according to one of Claims 3 to 14, characterized in that the regular body is a tetrahedron (16) with corners A, B, C, D and a center O, the edges AB, AC, AD, BC, CD, DB each have a center O _x , N, M, I, K, L and where the surfaces ABC, ACD, BCD, ABD each have a center E, F, G, H, and that the tetrahedron is formed by a chain or a ring of polyhedra BIO _x EO, CNIEO, AO _x NEO, ANMFO, CNKFO, DKMFO, BILGO, CIKGO, DKLGO, AO _x MHO, BO _x LHO, DLMHO, each connected by their edges AN, MO, KO, CK , IO, LO, LD, MO, O _x O, BO _x , IO, NO (Fig. 4). Stereometric structure according to one of claims 1 and 4 to 14, characterized in that the regular body is a dodecahedron (20; 22) which is formed by a chain or a ring of twelve polyhedra, each formed by one of the twelve pentagons on the surface of the dodecahedron (20; 22) and by the surfaces formed by the connection of the corners of this pentagon to the center O of the dodecahedron, and that the polyhedra are each connected via side edges of their pentagonal surfaces. Stereometric structure according to claim 20, characterized in that the corners AI, KN, O _x , PU of the dodecahedron (20) pentagons BKLME, MEFNS, NSUTO _x , NO _x GCF, FCABE, ACGHD, HGPTO _x , PHDIQ, DIKBA, IKLRQ, QRUTP , RUSML describe on its surface, which are each connected via their edges ME, SN, NO _x , FC, AC, HG, PH, DI, IK, QR, RU, LM (Fig. 6). Stereometric structure according to claim 20, characterized in that the corners AI, KN, O _x PU of the dodecahedron (22) pentagons BEMLK, BEFCA, BADIK, KIQRL, QRUTP, QPHDI, PHGO _x T, HGCAD, GCFNO _x , O _x NSUT, SURLM Describe, SMEFN on its surface, which are each connected via their edges BE, BA, KI, QR, QP, PH, HG, GC, O _x N, SU, SM, ME (Fig. 7). Stereometric structure according to one of claims 3 to 14, characterized in that the regular body is a dodecahedron (24; 26;) with corners AI, KN, O _x , PU, which delimit twelve pentagons on its surface, the edges KI, HG , EF, LM, PQ, NO _{x have} centers a, b, c, d, e, f, and that the dodecahedron (24; 26) is formed by a chain or ring of twenty-four polyhedra, each formed by half of one of the pentagons, the halving line running through the center points af and the opposite corner of the pentagon, and through the surfaces formed by connecting the corners of this pentagon half to the center O of the dodecahedron (24; 26). Stereometric structure according to claim 23, characterized in that the twenty-four polyhedra are connected via their edges Ac, cF, FN, Nf, Uf, O _x f, O _x G, Gb, Ab, Hb, HP, Pe, Ue, Qe, Ql , Ia, Aa, Ka, KL, Ld, Ud, Md, ME, Ec (Fig. 9). Stereometric structure according to claim 23, characterized in that the twenty-four polyhedra are connected by their edges AO, Fc, FN, Nf, UO, O _x f, O _x G, Gb, AO, Hb, HP, Pe, UO, Qe, Ql, Ia, AO, Ka, KL, Ld, UO, Md, ME, Ec. Stereometric structure according to one of claims 1 to 14, characterized in that the regular body is a rhombic dodecahedron (28; 30) with corners AI, KN, O _x , which is formed by a ring of twelve polyhedra, each formed by one of the twelve rhombuses on the surface of the rhombic dodecahedron (28; 30) and by the surfaces formed by connecting the corners of this rhombus with the center O of the rhombic dodecahedron (28; 30). Stereometric structure according to claim 26, characterized in that the polyhedra are connected via their edges FO, FL, CG, GO, GM, DH, HO, HN, EI, IO, IJ, BF. Stereometric structure according to claim 26, characterized in that the polyhedra are connected via their edges EB, HI, IK, BF, FC, KL, LM, GC, DG, NM, HN, ED. Stereometric structure according to one of Claims 1 to 14, characterized in that the regular body is an icosahedron with undivided triangles on its surface, the twenty polyhedra of which have edge connections, all of which lie on the surface of the icosahedron (Fig. 13). Stereometric structure according to one of claims 3 to 14, characterized in that the regular body is an icosahedron (34) with corners AI, KM and a center O, the edges BC, CD, DE, EF, FB, GH, HI, IK , KL each have a center point B ', C', D ', E', F ', G', H ', I', K ', L', and that the icosahedron is formed by a chain or ring of Polyhedra ACC'O, AC'DO, ADD'O, AD'EO, AEE'O, AE'FO, AFF'O, AF'BO, ABB'O, AB'CO, GBB'O, GB'CO, CGG'O, CG'HO, HCC'O, HC'DO, DHH'O, DH'IO, IDD'O, ID'EO, EII'O, EI ' KO, KEE'O, KE'FO, FKK'O, FK'LO, LFF'O, LF'BO, BLL'O, BL'GO, MGG'O, MG'HO, MHH'O, MH'IO, MII'O, MI'KO, MKK'O, MK'LO, MLL'O, ML'GO. Stereometric structure according to claim 30, characterized in that the polyhedra are connected via their edges AO, C'D, DH, HH ', MO, H'I, ID, DD', AO, D'E, EI, II ', MO , I'K, KE, EE ', AO, E'F, FK, KK', MO, K'L, LF, FF ', AO, F'B, BL, LL', MO, L'G, GB , BB ', AO, B'C, CG, GG', MO, G'H, HC, CC '. Sterometric structure according to claim 30, characterized in that the polyhedra are connected via their edges AC ', C'D, DH, HH', MH ', H'I, ID, DD', AD ', D'E, EI, II ', MI', I'K, KE, EE ', AE', E'F, FK, KK ', MK', K'L, LF, FF ', AF', F'B, BL, LL ', ML ', L'G, GB, BB', AB ', B'C, CG, GG', MG ', G'H, HC, CC'. Stereometric structure according to one of claims 1 to 14, characterized in that the regular body is an octahedron which is formed by twenty-four polyhedra, each of which is formed by a partial triangle of each triangle of the octahedron and by the connection of the corners of the partial triangle with the The center of the octahedron created surfaces. Stereometric structure according to claim 33, characterized in that each partial triangle is formed by two corner points of an octahedron triangle and the center of the octahedron triangle. Stereometric structure according to one of claims 1 to 14, characterized in that the regular body is an octahedron formed by twenty-four polyhedra, each formed by a partial quadrilateral of each triangle of the octahedron and by the connection of the corners of the part - Quadrilaterals with the center of the octahedron. Stereometric structure according to one of claims 1 to 14, characterized in that the regular body is a tetrahedron which is formed by eight polyhedra, each of which is formed by half of one of the triangles located on the surface of the tetrahedron and by the the connection of the corners of the triangle half to the center of the tetrahedron. Stereometric structure according to one of claims 1 to 14, characterized in that the regular body is a cube which is formed by eight polyhedra, which in turn are cubes (partial cubes). Polyhedron construction kit with a large number of polyhedra or parts of such polyhedra, which can be assembled into individual polyhedra, and hinge elements,
characterized, that one or more stereometric structures or stereometric toys according to one of the preceding claims can be produced with the polyhedron construction kit.

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