7-2 step prism

The 7-2 step prism is a convex isogonal polychoron and a member of the step prism family. It has 14 phyllic disphenoids of two different types as cells, with 8 joining at each vertex. It is the simplest step prism, excluding the pentachoron and the triangular duotegum, which are part of more specific families, as well as the only isogonal polychoron with 7 vertices. It is also the triangular funk tegum.

Vertex coordinates
Coordinates for the vertices of a 7-2 step prism inscribed in an heptagonal duoprism with base lengths a and b are given by: where k is an integer from 0 to 6. If the edge length differences are to be minimized, the ratio of a:b must be equivalent to :$$\sqrt{1-\frac{\sec\frac\pi7}{2}}$$ ≈ 1:0.66711.
 * (a*sin(2πk/7), a*cos(2πk/7), b*sin(4πk/7), b*cos(4πk/7)),

Measures
The hypervolume of a 7-2 step prism inscribed in an a×b duoprism is given by:
 * $$V=a^2b^2\xi,$$

where ξ ≈ 1.55622 is the largest real root of 884736x3–1613472x–823543, equivalent to 49/(192cos(2π/7)-96)-49/96.

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Phyllic disphenoid (7): 7-2 step prism
 * Scalene triangle (7): 7-2 step prism
 * Scalene triangle (14): 14-2 step prism
 * Edge (7): 7-2 step prism