Octagonal duoprism

The octagonal duoprism or odip, also known as the octagonal-octagonal duoprism, the 8 duoprism or the 8-8 duoprism, is a noble uniform duoprism that consists of 16 octagonal prisms and 64 vertices. It is also the digonal double gyrotrapezohedroid and the 16-7 gyrochoron. Together with its dual, it is the first in an infinite family of octagonal dihedral swirlchora.

The octagonal duoprism can be vertex-inscribed into a small rhombated tesseract or small prismatotetracontoctachoron.

This polychoron can be alternated into a square duoantiprism, although it cannot be made uniform. Eight of the octagons can also be alternated into long rectangles to create a square-square prismantiprismoid, which is also nonuniform.

Vertex coordinates
Coordinates for the vertices of an octagonal duoprism of edge length 1, centered at the origin, are given by:
 * (±1/2, ±(1+$\sqrt{2+√2}$)/2, ±1/2, ±(1+$\sqrt{2}$)/2),
 * (±1/2, ±(1+$\sqrt{2+√2}$)/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)).

Representations
An octagonal duoprism has the following Coxeter diagrams:


 * x8o x8o (full symmetry)
 * x4x x8o (BC2×I2(8) symmetry)
 * x4x x4x (BC2×BC2 symmetry, both octagons as ditetragons)
 * xwwx xxxx4xxxx&#xt (BC2×A1 axial, octagonal prism-first)

Related polychora
Non-adjacent cells of the octagonal duoprism can be augmented with square pucofastegiums. If 8 cells are augmented in this way, the result is the uniform small rhombated tesseract.