Journal for Geometry and Graphics 26 (2022), No. 1, 029--038
Copyright Heldermann Verlag 2022
How to Decide Whether Two Convex Octahedra are Affinely Equivalent Using Their Natural Developments Only
Victor Alexandrov
Sobolev Institute of Mathematics, Novosibirsk, Russia
and: Novosibirsk State University, Novosibirsk, Russia
alex@math.nsc.ru
Given two convex octahedra in Euclidean 3-space, we find conditions on their natural developments which are necessary and sufficient for these octahedra to be affinely equivalent to each other.
Keywords: Affine transformation, octahedron, natural development, Cayley–Menger determinant, spatial shape of a polyhedron.
MSC: 52C25; 52B10, 68U05.
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