Abstract
A chiral polyhedron with Schläfli symbol {p,q} is called tight if it has 2pq flags, which is the minimum possible. In this paper, we fully characterize the Schläfli symbols of tight chiral polyhedra. We also provide presentations for the automorphism groups of several families of tight chiral polyhedra.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. B. D’Azevedo, G. Jones and E. Schulte: Constructions of chiral polytopes of small rank, Canad. J. Math. 63 (2011), 1254–1283.
M. Conder: Chiral polytopes with up to 2000 ags, https://www.math.auckland.ac.nz/~conder/ChiralPolytopesWithFewFlags-ByType.txt
M. Conder and G. Cunningham: Tight orientably-regular polytopes, Ars Mathematica Contemporanea 8 (2015), 68–81.
G. Cunningham: Mixing chiral polytopes, J. Alg. Comb. 36 (2012), 263–277.
G. Cunningham: Minimal equivelar polytopes, Ars Mathematica Contemporanea 7 (2014), 299–315.
G. Cunningham and D. Pellicer: Classification of tight regular polyhedra, Journal of Algebraic Combinatorics 43 (2016), 665–691.
The GAP Group: GAP–Groups, Algorithms, and Programming, Version 4.4.12, 2008.
P. McMullen and E. Schulte: Abstract regular polytopes, Encyclopedia of Mathematics and its Applications, vol. 92, Cambridge University Press, Cambridge, 2002.
E. Schulte and A. I. Weiss: Chiral polytopes, Applied geometry and discrete mathematics, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., vol. 4, Amer. Math. Soc., Providence, RI, 1991, 493–516.