Decagonal duoexpandoprism

The decagonal duoexpandoprism or dedep is a convex isogonal polychoron and the ninth member of the duoexpandoprism family. It consists of 40 decagonal prisms of two kinds, 100 rectangular trapezoprisms, 200 wedges, and 100 tetragonal disphenoids. 2 decagonal prisms, 1 tetragonal disphenoids, 3 wedges, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal decagonal-icosagonal duoprisms, or more generally decagonal-didecagonal duoprisms, and a subset of its variations can be formed by expanding the cells of the decagonal duoprism outward. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{2}{1+\sqrt{\sqrt{130+58\sqrt5}-4\sqrt5-7}}$$ ≈ 1:1.41528.