229 research outputs found
Chiral extensions of chiral polytopes
Given a chiral d-polytope K with regular facets, we describe a construction
for a chiral (d + 1)-polytope P with facets isomorphic to K. Furthermore, P is
finite whenever K is finite. We provide explicit examples of chiral 4-polytopes
constructed in this way from chiral toroidal maps.Comment: 21 pages. [v2] includes several minor revisions for clarit
Polygonal Complexes and Graphs for Crystallographic Groups
The paper surveys highlights of the ongoing program to classify discrete
polyhedral structures in Euclidean 3-space by distinguished transitivity
properties of their symmetry groups, focussing in particular on various aspects
of the classification of regular polygonal complexes, chiral polyhedra, and
more generally, two-orbit polyhedra.Comment: 21 pages; In: Symmetry and Rigidity, (eds. R.Connelly, A.Ivic Weiss
and W.Whiteley), Fields Institute Communications, to appea
Minimal covers of the prisms and antiprisms
This paper contains a classication of the regular minimal abstract polytopes
that act as covers for the convex polyhedral prisms and antiprisms. It includes
a detailed discussion of their topological structure, and completes the
enumeration of such covers for convex uniform polyhedra. Additionally, this
paper addresses related structural questions in the theory of string C-groups.Comment: 22 pages, 8 figure
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