Chiral Polyhedra in Ordinary Space, II

A chiral polyhedron has a geometric symmetry group with two orbits on the flags, such that adjacent flags are in distinct orbits. Part I of the paper described the discrete chiral polyhedra in ordinary euclidean space E3 with finite skew faces and finite skew vertex-figures; they occur in infinite f...

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Bibliographic Details
Published in:Discrete & computational geometry 2005-08, Vol.34 (2), p.181-229
Main Author: Schulte, Egon
Format: Article
Language:English
Subjects:
Combinatorics
Geometry
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Summary:A chiral polyhedron has a geometric symmetry group with two orbits on the flags, such that adjacent flags are in distinct orbits. Part I of the paper described the discrete chiral polyhedra in ordinary euclidean space E3 with finite skew faces and finite skew vertex-figures; they occur in infinite families and are of types {4,6}, {6,4} and {6,6}. Part II completes the enumeration of all discrete chiral polyhedra in E3. There exist several families of chiral polyhedra of types {8,3} and {8,4} with infinite, helical faces. In particular, there are no discrete chiral polyhedra with finite faces in addition to those described in Part I.[PUBLICATION ABSTRACT]
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-005-1176-0