Discrete & Computational Geometry

, Volume 34, Issue 2, pp 181–229

Chiral Polyhedra in Ordinary Space, II


DOI: 10.1007/s00454-005-1176-0

Cite this article as:
Schulte, E. Discrete Comput Geom (2005) 34: 181. doi:10.1007/s00454-005-1176-0


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 {∞,3} and {∞,4} with infinite, helical faces. In particular, there are no discrete chiral polyhedra with finite faces in addition to those described in Part I.

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of Mathematics, Northeastern University, Boston, MA 02115 USA