Results in Mathematics

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

On regular polyhedra with hidden symmetries

  • Jörg M. Wills


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.


Riemann Surface Symmetry Group Automorphism Group Hide Symmetry Regular Polyhedron 
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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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