Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 44, No. 1, pp. 235-244 (2003)

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Construction of Non-Wythoffian Perfect 4-Polytopes

Gábor Gévay

Department of Geometry, University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, Hungary, e-mail: gevay@math.u-szeged.hu

Abstract: A polytope is perfect if its shape cannot be changed without changing the action of its symmetry group on its face-lattice. There was a conjecture by which perfect 4-polytopes formed a rather limited class of Wythoffian polytopes. It was disproved in a preceding paper of the author by showing that this class is much more wide. In the present paper we go even further by giving a construction that provides non-Wythoffian perfect 4-polytopes. The construction is based on including the copies of a suitable 3-polytope into the facets of a facet-transitive 4-polytope in a symmetry-preserving way.

Keywords: nodal polytope, perfect polytope, regular polytope, semi-nodal polytope, Wythoff's construction.

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Electronic version published on: 3 Apr 2003. This page was last modified: 4 May 2006.

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