Octagonal-decagonal duoprismatic prism

The octagonal-decagonal duoprismatic prism or oddip, also known as the octagonal-decagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 octagonal-decagonal duoprisms, 8 square-decagonal duoprisms, and 10 square-octagonal duoprisms. Each vertex joins 2 square-octagonal duoprisms, 2 square-decagonal duoprisms, and 1 octagonal-decagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

This polyteron can be alternated into a square-pentagonal duoantiprismatic antiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a pentagonal-square prismatic prismantiprismoid, which is also nonuniform.

Vertex coordinates
The vertices of an octagonal-decagonal duoprismatic prism of edge length 1 are given by all permutations of the first two coordinates of:
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,0,\,±\frac{1+\sqrt5}2,\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\frac12\right).$$

Representations
An octagonal-decagonal duoprismatic prism has the following Coxeter diagrams:
 * x x8o x10o (full symmetry)
 * x x4x x10o (BC2×I2(10)×A1 symmetry, octagons as ditetragons)
 * x x8o x5x (H2×I2(8)×A1 symmetry, decagons as dipentagons)
 * x x4x x5x (BC2×H2×A1 symmetry)
 * xx8oo xx10oo&#x (octagonal-decagonal duoprism atop octagonal-decagonal duoprism)
 * xx4xx xx10oo&#x
 * xx8oo xx5xx&#x
 * xx4xx xx5xx&#x