Dodecagonal duoexpandoprism

The dodecagonal duoexpandoprism or twaddep is a convex isogonal polychoron and the tenth member of the duoexpandoprism family. It consists of 48 dodecagonal prisms of two kinds, 144 rectangular trapezoprisms, 288 wedges, and 144 tetragonal disphenoids. 2 dodecagonal 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 dodecagonal-icositetragonal duoprisms, or more generaly dodecagonal-didodecagonal duoprisms, and a subset of its variations can be formed by expanding the cells of the dodecagonal duoprism outward. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{2}{1+\sqrt{2\sqrt{78+45\sqrt3}-8\sqrt3-11}}$$ ≈ 1:1.48709.