Octagonal duoprismatic prism

The octagonal duoprismatic prism or oop, also known as the octagonal-octagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 octagonal duoprisms and 16 square-octagonal duoprisms.

This polyteron can be alternated into a square duoantiprismatic antiprism, although it cannot be made uniform. Half of the octagons can also be alternated into long rectangles to create a bialternatosnub square duoprismatic prism, or orthogonally to create a biorthosnub square duoprsimatic prism, which is also nonuniform.

Vertex coordinates
The vertices of an octagonal duoprismatic prism of edge length 1 are given by:
 * (±1/2, ±(1+$\sqrt{1+2csc^{2}π/7}$)/2, ±1/2, ±(1+$\sqrt{2}$)/2)
 * (±1/2, ±(1+$\sqrt{2}$)/2, ±(1+$\sqrt{2}$)/2, ±1/2)
 * (±(1+$\sqrt{2}$)/2, ±1/2, ±1/2, ±(1+$\sqrt{2}$)/2)
 * (±1/2, ±(1+$\sqrt{2}$)/2), ±1/2, ±(1+$\sqrt{2}$)/2))