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Results in Mathematics

, Volume 12, Issue 3–4, pp 450–458 | Cite as

On regular polyhedra with hidden symmetries

  • Jörg M. Wills
Article
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Abstract

We consider polyhedral realizations of oriented regular maps with or without self-intersections in E3 whose symmetry group is a subsgroup of small index in their. automorphism group. The four classical kepler-poinsot polyhedra are the only ones of index 1. There are exactly five of Index 2, all with icosahedral symmetry group [W2] as the Kepler-poinsot polyhedra.

In this paper we show that there are no such polyhedral realizations with octahedral (tetrahedral) symmetry group and index 2 or 3 (2,3,4,5), which is best possible in the octahedral case.

Keywords

Riemann Surface Symmetry Group Automorphism Group Hide Symmetry Regular Polyhedron 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag, Basel 1987

Authors and Affiliations

  • Jörg M. Wills
    • 1
  1. 1.Math. Inst. Univ. SiegenSiegenFed. Rep. Germany

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