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An example of a flexible polyhedron with nonconstant volume in the spherical space. (English) Zbl 0881.52007

The recently established Bellows Conjecture asserts that each oriented flexible polyhedron in \(\mathbb{E}^3\) conserves its volume during a flex. It is also known that each flexible polyhedron in \(\mathbb{E}^3\) conserves its mean curvature during a flex.
In this paper the author constructs a flexible polyhedron in an open half-sphere \(\mathbb{S}^3_+\) which conserves neither volume nor mean curvature during a flex.
The polyhedron is a modification of a polyhedron constructed from four spherical digons in \(\mathbb{S}^3\).

MSC:

52B11 \(n\)-dimensional polytopes
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