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EP0787514A2 - Jouet stéréometrique, structure stéréometrique, en particulier jouet stéréometrique - Google Patents

Jouet stéréometrique, structure stéréometrique, en particulier jouet stéréometrique Download PDF

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Publication number
EP0787514A2
EP0787514A2 EP97101652A EP97101652A EP0787514A2 EP 0787514 A2 EP0787514 A2 EP 0787514A2 EP 97101652 A EP97101652 A EP 97101652A EP 97101652 A EP97101652 A EP 97101652A EP 0787514 A2 EP0787514 A2 EP 0787514A2
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EP
European Patent Office
Prior art keywords
stereometric
polyhedra
structure according
edges
ring
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
Application number
EP97101652A
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German (de)
English (en)
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EP0787514A3 (fr
Inventor
Hartmut Endlich
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Individual
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Individual
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Filing date
Publication date
Application filed by Individual filed Critical Individual
Publication of EP0787514A2 publication Critical patent/EP0787514A2/fr
Publication of EP0787514A3 publication Critical patent/EP0787514A3/fr
Withdrawn legal-status Critical Current

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    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63F—CARD, BOARD, OR ROULETTE GAMES; INDOOR GAMES USING SMALL MOVING PLAYING BODIES; VIDEO GAMES; GAMES NOT OTHERWISE PROVIDED FOR
    • A63F9/00—Games not otherwise provided for
    • A63F9/06—Patience; Other games for self-amusement
    • A63F9/08—Puzzles provided with elements movable in relation, i.e. movably connected, to each other
    • A63F9/088—Puzzles with elements that are connected by straps, strings or hinges, e.g. Rubik's Magic

Definitions

  • 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.
  • 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.
  • 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.
  • this toy does not form a closed unit, so that there is a risk that individual elements can be lost.
  • kaleidocycles 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.
  • a polyhedron ring which is a cube in its basic position.
  • 6 of its 12 polyhedron edge connections lie on cube edges, the other 6 on diagonals of the cube.
  • 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.
  • the cube can only be opened to a ring with a very small opening.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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".
  • “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.
  • 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.
  • 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.
  • the surfaces can be designed in relief rather than smooth or imperfect (for example with cut corners or with holes in the middle).
  • 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).
  • 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.
  • 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).
  • 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.
  • 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.
  • connection at corners of the polyhedra which would possibly increase the mobility and complexity of the toy.
  • the connection at edges has the advantages of particularly simple manufacture and handling and produces greater regularity in handling the toy.
  • each polyhedron is connected to another polyhedron at two different edges.
  • the desired chain structure or ring structure is achieved in a particularly simple manner.
  • 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.
  • 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.
  • the basic position is a cube and that at least twelve polyhedron connecting edges lie on edges of the cube.
  • 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.
  • the arrangement is such that only six polyhedron connections lie on cube edges.
  • 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.
  • the polyhedra completely fill the regular body in the basic position.
  • 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.
  • 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.
  • a cube can be turned inside out into a pentagon dodecahedron.
  • 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.
  • the ring can be turned inside out.
  • 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.
  • the ring can be "rotated” by 360 °.
  • at least some of the realizable stereometric toys according to the invention can be "turned out” based on a certain inverted state.
  • 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.
  • 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 .
  • 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.
  • 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.
  • the polyhedron ring is not completely invertible, so that the variability of this toy compared to the other embodiments of the invention remains.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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
  • the alternative chaining variants described above show a certain regularity and are therefore particularly preferred.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • polyhedra via their edges EB, HI, IK, BF, FC, KL, LM, GC, DG, NM, HN, ED.
  • 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.
  • 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
  • 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'.
  • 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 '.
  • 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.
  • 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.
  • FIG. 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.
  • FIG. 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.
  • 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.
  • 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.
  • 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.
  • FIG. 9 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.
  • 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.
  • FIG. 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.
  • 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.
  • FIG. 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,
  • 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'.
  • the connecting edges also lie inside the icosahedron 34.
  • 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'.
  • 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.
  • each triangle of the octahedron has a center.
  • 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.
  • 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.
  • the edge 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.
  • FIG. 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.
  • edge connections can be formed by film hinges.
  • hinges made of fabric tape or the like are also conceivable.
  • 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.
  • the connecting means are snap-in connections so that the hinges can be releasably connected to the edges.
  • 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.
  • 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.
  • the polyhedra are determined by simple symmetrical structuring of the regular body, including the center of the regular body.
  • 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.
  • the ring found can be turned into a hollow shape.
  • known shapes can be excluded.
  • 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).
  • a possible polyhedral ring cannot be turned inside out (second step).
  • 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.
  • the simplest division of space 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.
  • FIG. 20. 20h shows an eight-part cube.

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  • Engineering & Computer Science (AREA)
  • Multimedia (AREA)
  • Toys (AREA)
EP97101652A 1996-02-02 1997-02-03 Jouet stéréometrique, structure stéréometrique, en particulier jouet stéréometrique Withdrawn EP0787514A3 (fr)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
DE19603825 1996-02-02
DE1996103825 DE19603825A1 (de) 1996-02-02 1996-02-02 Stereometriespielzeug

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EP0787514A2 true EP0787514A2 (fr) 1997-08-06
EP0787514A3 EP0787514A3 (fr) 1997-12-03

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Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR2793160A1 (fr) * 1999-05-07 2000-11-10 Raymond Bohec Perfectionnement d'un dispositif d'assemblage en configurations multiples de prismes articules entre eux par des charnieres reliant chacune deux de leurs aretes
WO2001039853A1 (fr) * 1999-12-04 2001-06-07 Felix Pfister Mecanisme polyedre et son procede de production
WO2002005913A1 (fr) 2000-07-05 2002-01-24 Robert Burrell Byrnes Jouets
ITUB20161146A1 (it) * 2016-02-29 2017-08-29 Michela Cascioli Accessorio ornamentale, particolarmente del tipo a funzionalità incrementata.
US11524222B2 (en) * 2018-11-21 2022-12-13 Hanayama International Trading Limited Polyhedral toy

Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB2107200A (en) * 1981-09-29 1983-04-27 Asahi Tsusho Kk Polytetrahedron toy device
GB2108395A (en) * 1981-10-19 1983-05-18 Karran Products Ltd Polytetrahedral chain device
GB2111395A (en) * 1981-11-12 1983-07-06 Kam Cheung Siu Manipulative puzzle
FR2614210A1 (fr) * 1987-04-22 1988-10-28 Beroff Andre Structure constituee de modules polyedriques articules avec moyens de maintien en forme utilisable notamment comme jeu.
DE8912392U1 (de) * 1989-10-18 1990-03-01 Ritzenfeld, Albert, Innsbruck Kaleidozyklus
DE9012332U1 (de) * 1990-08-28 1990-11-15 Asch, Sabine, 7120 Bietigheim-Bissingen Dreidimensionales Puzzle
US5104125A (en) * 1990-01-16 1992-04-14 John Wilson Three-dimensional polyhedral jigsaw-type puzzle
WO1992011911A1 (fr) * 1991-01-08 1992-07-23 Klaus Dieter Pfeffer Corps de transformation

Patent Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB2107200A (en) * 1981-09-29 1983-04-27 Asahi Tsusho Kk Polytetrahedron toy device
GB2108395A (en) * 1981-10-19 1983-05-18 Karran Products Ltd Polytetrahedral chain device
GB2111395A (en) * 1981-11-12 1983-07-06 Kam Cheung Siu Manipulative puzzle
FR2614210A1 (fr) * 1987-04-22 1988-10-28 Beroff Andre Structure constituee de modules polyedriques articules avec moyens de maintien en forme utilisable notamment comme jeu.
DE8912392U1 (de) * 1989-10-18 1990-03-01 Ritzenfeld, Albert, Innsbruck Kaleidozyklus
US5104125A (en) * 1990-01-16 1992-04-14 John Wilson Three-dimensional polyhedral jigsaw-type puzzle
DE9012332U1 (de) * 1990-08-28 1990-11-15 Asch, Sabine, 7120 Bietigheim-Bissingen Dreidimensionales Puzzle
WO1992011911A1 (fr) * 1991-01-08 1992-07-23 Klaus Dieter Pfeffer Corps de transformation

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR2793160A1 (fr) * 1999-05-07 2000-11-10 Raymond Bohec Perfectionnement d'un dispositif d'assemblage en configurations multiples de prismes articules entre eux par des charnieres reliant chacune deux de leurs aretes
WO2000067861A1 (fr) * 1999-05-07 2000-11-16 Raymond Bohec Dispositif d'assemblage en configurations multiples de prismes articules entre eux
WO2001039853A1 (fr) * 1999-12-04 2001-06-07 Felix Pfister Mecanisme polyedre et son procede de production
WO2002005913A1 (fr) 2000-07-05 2002-01-24 Robert Burrell Byrnes Jouets
ITUB20161146A1 (it) * 2016-02-29 2017-08-29 Michela Cascioli Accessorio ornamentale, particolarmente del tipo a funzionalità incrementata.
US11524222B2 (en) * 2018-11-21 2022-12-13 Hanayama International Trading Limited Polyhedral toy

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EP0787514A3 (fr) 1997-12-03
DE19603825A1 (de) 1997-08-07

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