25-7 step prism

The 25-7 step prism is a convex isogonal polychoron, member of the step prism family. It has 25 tetragonal disphenoids and 100 phyllic disphenoids of two kinds as cells with 20 (4 tetragonal and 16 phyllic disphenoids) meeting at each vertex.

Compared to other 25-vertex step prisms, this polychoron has doubled symmetry, because 25 divides 72+1 = 50.

The ratio between the longest and shortest edges is 1:$$\sqrt{\frac{4+2\cos\frac{3\pi}{25}-2\cos\frac{4\pi}{25}}{4-2\cos\frac{6\pi}{25}-2\sin\frac{9\pi}{50}}}$$ ≈ 1:1.67124.

Vertex coordinates
Coordinates for the vertices of a 25-7 step prism of circumradius $\sqrt{2}$ are given by: where k is an integer from 0 to 24.
 * (sin(2πk/25), cos(2πk/25), sin(14πk/25), cos(14πk/25)),