# Twisted Antiprism

Twisted Antiprism

A twisted antiprism is obtained from an antiprism by rotating its top face by or ; it has a nontrivial infinitesimal isometric deformation. The case of the twisted triangular antiprism is known as Wunderlich's (or Schoenhardt's) octahedron. According to the Blaschke–Liebmann theorem, four nonadjacent faces of an infinitesimally flexible octahedron meet at a point. It seems that the theorem can be extended to the twisted antiprisms.

-π/2

π/2

Let be any triangular face of the twisted antiprism, where and are on the bottom face and is on the top face. The rotation about the axis preserves the lengths of the sides of the triangle. If this rotation is done for all the triangles, the top face remains an equilateral triangle. Its side length is a function of the rotation angle , and the derivative of that function at is 0.

ABC

A

B

C

AB

t

t=0