Rigidity and flexibility of virtual polytopes

G. Panina

Open Mathematics (2003)

  • Volume: 1, Issue: 2, page 157-168
  • ISSN: 2391-5455

Abstract

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All 3-dimensional convex polytopes are known to be rigid. Still their Minkowski differences (virtual polytopes) can be flexible with any finite freedom degree. We derive some sufficient rigidity conditions for virtual polytopes and present some examples of flexible ones. For example, Bricard's first and second flexible octahedra can be supplied by the structure of a virtual polytope.

How to cite

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G. Panina. "Rigidity and flexibility of virtual polytopes." Open Mathematics 1.2 (2003): 157-168. <http://eudml.org/doc/268858>.

@article{G2003,
abstract = {All 3-dimensional convex polytopes are known to be rigid. Still their Minkowski differences (virtual polytopes) can be flexible with any finite freedom degree. We derive some sufficient rigidity conditions for virtual polytopes and present some examples of flexible ones. For example, Bricard's first and second flexible octahedra can be supplied by the structure of a virtual polytope.},
author = {G. Panina},
journal = {Open Mathematics},
keywords = {Virtual polytope; rigidity; flexion; Bricard's octahedron; MSC (2000); 52C25; polytopal function; Bricard's flexible octahedron; Minkowski addition; Grothendieck group; support function; normal vector; connected fan; disconnected net; Cauchy lemma; Euler characteristic; virtual polytope; rigidity theorem; flexible virtual polytopes},
language = {eng},
number = {2},
pages = {157-168},
title = {Rigidity and flexibility of virtual polytopes},
url = {http://eudml.org/doc/268858},
volume = {1},
year = {2003},
}

TY - JOUR
AU - G. Panina
TI - Rigidity and flexibility of virtual polytopes
JO - Open Mathematics
PY - 2003
VL - 1
IS - 2
SP - 157
EP - 168
AB - All 3-dimensional convex polytopes are known to be rigid. Still their Minkowski differences (virtual polytopes) can be flexible with any finite freedom degree. We derive some sufficient rigidity conditions for virtual polytopes and present some examples of flexible ones. For example, Bricard's first and second flexible octahedra can be supplied by the structure of a virtual polytope.
LA - eng
KW - Virtual polytope; rigidity; flexion; Bricard's octahedron; MSC (2000); 52C25; polytopal function; Bricard's flexible octahedron; Minkowski addition; Grothendieck group; support function; normal vector; connected fan; disconnected net; Cauchy lemma; Euler characteristic; virtual polytope; rigidity theorem; flexible virtual polytopes
UR - http://eudml.org/doc/268858
ER -

References

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