Solution of the Sz�kefalvi-Nagy problem for a class of convex polytopes

Baladze, E D

doi:10.1007/bf01263533

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Belt Polytopes and Angle Vectors1

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1995

2023

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Cited by 5 publications

(2 citation statements)

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“…We are now going to formulate the results that were established in [3] and [4], but first we describe two classes of the convex bodies (see [5]- [7]). Definition 2.…”

Section: Theorem 2 (Boltyanski) Let M C R D Be a Compact Centrally mentioning

confidence: 99%

A new step in the solution of the Szökefalvi-Nagy problem

Boltyanski

1992

Discrete Comput Geom

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“…We are now going to formulate the results that were established in [3] and [4], but first we describe two classes of the convex bodies (see [5]- [7]). Definition 2.…”

Section: Theorem 2 (Boltyanski) Let M C R D Be a Compact Centrally mentioning

confidence: 99%

A new step in the solution of the Szökefalvi-Nagy problem

Boltyanski

1992

Discrete Comput Geom

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“…A polytope P ⊂ R d is a belt polytope (or generalized zonotope) if and only if every 2-face F ⊂ P has an even number of edges and antipodal edges are parallel. Belt polytopes were studied by Baladze [4] (see also [10]) and are equivalently characterized by the fact that their normal fans are given by a hyperplane arrangement.…”

Section: Belt Polytopes and Angle Vectorsmentioning

confidence: 99%

Generalized angle vectors, geometric lattices, and flag-angles

Backman¹,

Manecke²,

Sanyal³

2018

Preprint

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Interior angle vectors of polytopes are semi-discrete analogs of f -vectors that take into account the interior angles at faces measured by spherical volumes. In this context, Gram's relation takes the place of the Euler-Poincaré relation as the unique linear relation among the entries of the interior angle vectors. Simple and normalized cone valuations naturally generalize spherical volumes, and in this paper we study the associated interior and exterior angle vectors. We show that for any given cone valuation, Gram's relation is the unique linear relation that is satisfied by all generalized interior angle vectors. To show uniqueness, we prove that the angle vectors of a zonotope are independent of the cone valuation and only depend on the combinatorics of the zonotope.In the second part of the paper, we introduce flag-angle vectors as a counterpart to flag-vectors of polytopes. We determine the linear relations on flag-angle vectors and we show a connection to flag-vectors of lattices of flats.

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Combinatorial geometry of belt bodies

Boltyanski

Martini

1995

Results. Math.

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Solution of the Sz�kefalvi-Nagy problem for a class of convex polytopes

Cited by 5 publications

References 4 publications

A new step in the solution of the Szökefalvi-Nagy problem

A new step in the solution of the Szökefalvi-Nagy problem

Generalized angle vectors, geometric lattices, and flag-angles

Combinatorial geometry of belt bodies

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