Octagonal ditetragoltriate

The octagonal ditetragoltriate is a convex isogonal polychoron and the sixth member of the ditetragoltriates that consists of 16 octagonal prisms and 64 rectangular trapezoprisms. However, it cannot be made uniform. It is the first in an infinite family of isogonal octagonal prismatic swirlchora.

This polychoron can be alternated into a square double antiprismoid, which is also nonuniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:(2+$\sqrt{4-2√2}$)/2 ≈ 1:1.54120.

Vertex coordinates
The vertices of an octagonal ditetragoltriate, assuming that the trapezoids have three equal edges of length 1, centered at the origin, are given by:
 * (±1/2, ±(1+$\sqrt{2}$)/2, ±(2+$\sqrt{4-2√2}$)/4, ±(2+2$\sqrt{2}$+$\sqrt{4+2√2}$)/4),
 * (±1/2, ±(1+$\sqrt{2}$)/2, ±(2+2$\sqrt{2}$+$\sqrt{4+2√2}$)/4, ±(2+$\sqrt{4-2√2}$)/4),
 * (±(1+$\sqrt{2}$)/2, ±1/2, ±(2+$\sqrt{4-2√2}$)/4, ±(2+2$\sqrt{2}$+$\sqrt{4+2√2}$)/4),
 * (±(1+$\sqrt{2}$)/2, ±1/2, ±(2+2$\sqrt{2}$+$\sqrt{4+2√2}$)/4, ±(2+$\sqrt{4-2√2}$)/4),
 * (±(2+$\sqrt{4-2√2}$)/4, ±(2+2$\sqrt{2}$+$\sqrt{4+2√2}$)/4, ±1/2, ±(1+$\sqrt{2}$)/2),
 * (±(2+$\sqrt{4-2√2}$)/4, ±(2+2$\sqrt{2}$+$\sqrt{4+2√2}$)/4, ±(1+$\sqrt{2}$)/2, ±1/2),
 * (±(2+2$\sqrt{2}$+$\sqrt{4+2√2}$)/4, ±(2+$\sqrt{4-2√2}$)/4, ±1/2, ±(1+$\sqrt{2}$)/2),
 * (±(2+2$\sqrt{2}$+$\sqrt{4+2√2}$)/4, ±(2+$\sqrt{4-2√2}$)/4, ±(1+$\sqrt{2}$)/2, ±1/2).

Category:Octagonal prismatic swirlchora]]