Discrete & Computational Geometry

, Volume 44, Issue 1, pp 167–194 | Cite as

Combinatorial Structure of Schulte’s Chiral Polyhedra



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 chiral Geometrically chiral Chiral polyhedron Geometric polyhedron 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.York UniversityTorontoCanada

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