Digonal-octagonal tetraalterantiprismoid

The digonal-octagonal tetraalterantiprismoid is a convex isogonal polychoron that consists of 8 rectangular antiprisms, 8 tetragonal disphenoids, 8 rhombic disphenoids, 48 phyllic disphenoids of three kinds, and 32 irregular tetrahedra. 2 rectangular antiprisms, 1 tetragonal disphenoid, 1 rhombic disphenoid, 6 phyllic disphenoids, and 4 irregular tetrahedra join at each vertex. It can be obtained as a subsymmetrical faceting of the octagonal-hexadecagonal duoprism. However, it cannot be made uniform.

This polychoron cannot be optimized using the ratio method, because the solution (with intended minimal ratio 1:$$\sqrt{1+\sqrt2}$$ ≈ 1:1.55377) would yield a square-square duoantiprism instead.