# Rigidity and flexibility of virtual polytopes

Open Mathematics (2003)

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

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topG. 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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