Hendecagonal duoexpandoprism

The hendecagonal duoexpandoprism or hendep is a convex isogonal polychoron and the tenth member of the duoexpandoprism family. It consists of 44 hendecagonal prisms of two kinds, 121 rectangular trapezoprisms, 242 wedges, and 121 tetragonal disphenoids. 2 hendecagonal 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 hendecagonal-icosidigonal duoprisms, or more generally hendecagonal-dihendecagonal duoprisms, and a subset of its variations can be obtained by expanding the cells of the hendecagonal duoprism outward. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{2}{1+{\tan\frac{\pi}{22}}\sqrt{3+4\cos\frac{\pi}{11}}}$$ ≈ 1:1.45352.