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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