Inscribing a regular octahedron into polytopes

Abstract

We prove that any simple polytope (and some non-simple polytopes) in ${\mathbb{R}}^3$ admits an inscribed regular octahedron.

References in corpus (4)

• The discrete square peg problem
• Inscribing a regular crosspolytope
• Equipartition of a measure by $(Z_p{)}^k$-invariant fans
• Knaster's problem for $(Z_2{)}^k$-symmetric subsets of the sphere $S^{2^k-1}$

Cited by in corpus (3)

• Configuration Spaces, Multijet Transversality, and the Square-Peg Problem
• Inscribed triangles of Jordan curves in ${\mathbb{R}}^n$
• Families of similar simplices inscribed in most smoothly embedded spheres