Dodecagonal duotransitionalterprism

Dodecagonal duotransitionalterprism
Rank	4
Type	Isogonal
Space	Spherical
Elements
Cells	144 rectangular trapezoprisms, 24 dodecagonal prisms, 24 dodecagonal trapezorhombihedra
Faces	576 isosceles trapezoids, 288 rectangles, 144 squares, 48 dodecagons
Edges	288+576+576
Vertices	576
Vertex figure	Isosceles trapezoidal pyramid
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Dodecagonal duotransitionaltertegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(12)≀S2, order 1152
Convex	Yes
Nature	Tame

The dodecagonal duotransitionalterprism is a convex isogonal polychoron and the eleventh member of the duotransitionalterprism family. It consists of 24 dodecagonal trapezorhombihedra, 24 dodecagonal prisms, and 144 rectangular trapezoprisms. 2 dodecagonal trapezorhombihedra, 1 dodecagonal prism, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal dodecagonal-didoecagonal duoprisms. However, it cannot be made scaliform.

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

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$\frac{3+\sqrt3}{2}$ ≈ 1:2.36603.