Annals of Combinatorics 1 (1997) 261-278


Flat Regular Polytopes

Peter McMullen and Egon Schulte

Department of Mathematics, University College London Gower Street, London WCIE 6BT, England
p.mcmullen@ucl.ac.uk

Department of Mathematics, Northeastern University, Boston, MA 02115, USA
schulte@neu.edu

Received April 11, 1997

AMS Subject Classification: 51M20

With best wishes to H.S.M. Coxeter for his 90th birthday.

Abstract. At the centre of the theory of abstract regular polytopes lies the amalgamation problem: given two regular n-polytopes P1 and P2, when does there exist a regular (n+1)-polytope P whose facets are isomorphic to P1 and whose vertex-figures are isomorphic to P2? The most general circumstances known hitherto which lead to a positive answer involve flat polytopes, which are such that each vertex lies in each facet. The object of this paper is to describe an analogous but wider class of constructions, which generalize the previous results.

Keywords: polyhedra and polytopes, regular figures, division of space


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