Back faces of a face polytope

Back faces of a face polytope

Full-dimensional cones of polytopal fans are spanned by invisible facets of face polytopes. However invisible faces cannot perform the same function for cones of lower dimension. It makes difficult considering fans with low-dimensional cones in any consistent manner. The paper defines back faces of...

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Veröffentlicht in:Lobachevskii journal of mathematics 2015-04, Vol.36 (2), p.190-197
1. Verfasser: Matveev, M. N.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
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container_title Lobachevskii journal of mathematics
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creator Matveev, M. N.
description Full-dimensional cones of polytopal fans are spanned by invisible facets of face polytopes. However invisible faces cannot perform the same function for cones of lower dimension. It makes difficult considering fans with low-dimensional cones in any consistent manner. The paper defines back faces of a polytope so that they can be used as faces spanning cones of a polytopal fan regardless of dimension. As an application of back faces a theorem is proved according to which some positive combination of solid face polytopes flattens, becomes a plane face polytope.
doi_str_mv 10.1134/S1995080215020134
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subjects Algebra
Analysis
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
title Back faces of a face polytope
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