Discrete & Computational Geometry

, Volume 44, Issue 1, pp 167–194

Combinatorial Structure of Schulte’s Chiral Polyhedra


DOI: 10.1007/s00454-010-9247-2

Cite this article as:
Pellicer, D. & Ivić Weiss, A. Discrete Comput Geom (2010) 44: 167. doi:10.1007/s00454-010-9247-2


Schulte classified the discrete chiral polyhedra in Euclidean 3-space and showed that they belong to six families. The polyhedra in three of the families have finite faces and the other three families consist of polyhedra with (infinite) helical faces. We show that all the chiral polyhedra with finite faces are combinatorially chiral. However, the chiral polyhedra with helical faces are combinatorially regular. Moreover, any two such polyhedra with helical faces in the same family are isomorphic.


Combinatorially chiralGeometrically chiralChiral polyhedronGeometric polyhedron

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.York UniversityTorontoCanada