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.
@article{bwmeta1.element.doi-10_2478_BF02476005,
author = {G. Panina},
title = {Rigidity and flexibility of virtual polytopes},
journal = {Open Mathematics},
volume = {1},
year = {2003},
pages = {157-168},
zbl = {1032.52011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02476005}
}
G. Panina. Rigidity and flexibility of virtual polytopes. Open Mathematics, Tome 1 (2003) pp. 157-168. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02476005/
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