Extensions of regular polytopes with preassigned Schläfli symbol |
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Authors: | Daniel Pellicer |
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Affiliation: | Universidad Nacional Autónoma de México, Mexico, DF 04510, Mexico |
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Abstract: | We say that a (d+1)-polytope P is an extension of a polytope K if the facets or the vertex figures of P are isomorphic to K. The Schläfli symbol of any regular extension of a regular polytope is determined except for its first or last entry. For any regular polytope K we construct regular extensions with any even number as first entry of the Schläfli symbol. These extensions are lattices if K is a lattice. Moreover, using the so-called CPR graphs we provide a more general way of constructing extensions of polytopes. |
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Keywords: | Extensions Abstract regular polytopes |
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