8-2 step prism

The 8-2 step prism is a convex isogonal polychoron and a member of the step prism family. It has 4 rhombic disphenoids and 16 phyllic disphenoids of two kinds as cells, with a total of 10 (2 rhombic and 8 phyllic disphenoids) joining at each vertex. It is one of 3 isogonal polychora with 8 vertices, and the only one not to be uniform (the other 2 are the hexadecachoron and tetrahedral prism).

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$\sqrt{6+2√2}$/2 ≈ 1:1.48563.

Vertex coordinates
Coordinates for the vertices of an 8-2 step prism inscribed in an octagonal duoprism with base lengths a and b are given by: where k is an integer from 0 to 7. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to 1:$$\frac{\sqrt{4+2\sqrt2}}{2}$$ ≈ 1:1.30656.
 * (a*sin(πk/4), a*cos(πk/4), b*sin(πk/2), b*cos(πk/2)),

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Phyllic disphenoid (8): 8-2 step prism
 * Scalene triangle (8): 8-2 step prism
 * Scalene triangle (16): 16-2 step prism
 * Edge (8): 8-2 step prism