Octagonal duoexpandoprism

The octagonal duoexpandoprism or odep is a convex isogonal polychoron and the sixth member of the duoexpandoprism family. It consists of 32 octagonal prisms of two kinds, 64 rectangular trapezoprisms, 128 wedges and 64 tetragonal disphenoids. 2 octagonal prisms, 1 tetragonal disphenoid, 3 wedges, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal octagonal-hexadecagonal duoprisms, or more generally octagonal-dioctagonal duoprisms, and a subset of its variations can be formed by expanding the cell of the octagonal duoprism outward. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{2}{1+\sqrt{2\sqrt{10+7\sqrt2}-4\sqrt2-3}}$$ ≈ 1:1.32039.