Digonal duotransitionalterantiprism

Digonal duotransitionalterantiprism
File:Digonal duotransitionalterantiprism.png
Rank	4
Type	Isogonal
Elements
Cells	8+16 tetragonal disphenoids, 32 isosceles trapezoidal pyramids, 8 biwedges
Faces	32+32+64 isosceles triangles, 32 isosceles trapezoids
Edges	16+16+32+64
Vertices	32
Vertex figure	Polyhedron with 2 tetragons and 8 triangles
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Digonal duotransitionalterantitegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B2+≀S2×2, order 64
Convex	Yes
Nature	Tame

The digonal duotransitionalterantiprism is a convex isogonal polychoron and the first member of the duotransitionalterantiprism family. It consists of 8 biwedges, 32 isosceles trapezoidal pyramids, and 24 tetragonal disphenoids of two kinds. 2 biwedges, 3 tetragonal dispheniods, and 5 isosceles trapezoidal pyramids join at each vetex. It can be obtained as an alternation of the square duotransitionalterprism. However, it cannot be made scaliform.

This polychoron cannot be optimized using the ratio method, because the solution (with intended minimal ratio 1:${\sqrt {2}}$ ≈ 1:1.41421) would yield a rectified tesseract instead.