Hexagonal duotransitionalterprism

Hexagonal duotransitionalterprism
Rank	4
Type	Isogonal
Elements
Cells	36 rectangular trapezoprisms, 12 hexagonal prisms, 12 hexagonal trapezorhombihedra
Faces	144 isosceles trapezoids, 72 rectangles, 36 squares, 24 hexagons
Edges	72+144+144
Vertices	144
Vertex figure	Isosceles trapezoidal pyramid
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Hexagonal duotransitionaltertegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	G2≀S2, order 288
Convex	Yes
Nature	Tame

The hexagonal duotransitionalterprism is a convex isogonal polychoron and the fifth member of the duotransitionalterprism family. It consists of 12 hexagonal trapezorhombihedra, 12 hexagonal prisms, and 36 rectangular trapezoprisms. 2 hexagonal trapezorhombihedra, 1 hexagonal prism, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal hexagonal-dihexagonal duoprisms. However, it cannot be made scaliform.

This polychoron can be alternated into a triangular duotransitionalterantiprism, which is also not scaliform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:${\frac {2+{\sqrt {6}}}{2}}$ ≈ 1:2.22474.