Glasnik Matematicki, Vol. 47, No. 2 (2012), 421-430.

ON THE SIZE OF EQUIFACETTED SEMI-REGULAR POLYTOPES

Tomaž Pisanski, Egon Schulte and Asia Ivić Weiss

Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia

Department of Mathematics, Northeastern University, Boston, Massachusetts, USA, 02115

Department of Mathematics and Statistics, York University, Toronto, ON, Canada M3J 1P3

Abstract.   Unlike the situation in the classical theory of convex polytopes, there is a wealth of semi-regular abstract polytopes, including interesting examples exhibiting some unexpected phenomena. We prove that even an equifacetted semi-regular abstract polytope can have an arbitrary large number of flag orbits or face orbits under its combinatorial automorphism group.

2010 Mathematics Subject Classification.   51M20, 52B15.

Key words and phrases.   Semi-regular polytope, uniform polytope, Archimedean solid, abstract polytope.

Full text (PDF) (free access)

DOI: 10.3336/gm.47.2.15

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