Dodecagonal antiditetragoltriate

Dodecagonal antiditetragoltriate
(OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Notation
Bowers style acronym	Twadet
Elements
Cells	144+144 tetragonal disphenoids, 288 rectangular pyramids, 24 dodecagonal prisms
Faces	576+576 isosceles triangles, 288 rectangles, 24 dodecagons
Edges	288+288+576
Vertices	288
Vertex figure	Biaugmented triangular prism
Measures (based on same duoprisms as optimized dodecagonal ditetragoltriate)
Edge lengths	Edges of smaller dodecagon (288): 1
	Lacing edges (576): $\sqrt{11+6\sqrt3-\sqrt{194+112\sqrt3}} ≈ 1.30186$
	Edges of larger dodecagon (288): $\frac{1+\sqrt3}{2} ≈ 1.36603$
Circumradius	$\sqrt{\frac{11+6\sqrt3}{2}} ≈ 3.27050$
Central density	1
Related polytopes
Army	Twadet
Regiment	Twadet
Dual	Dodecagonal antitetrambitriate
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(12)≀S2, order 1152
Convex	Yes
Nature	Tame

The dodecagonal antiditetragoltriate or twadet is a convex isogonal polychoron and the tenth member of the antiditetragoltriate family. It consists of 24 dodecagonal prisms, 288 rectangular pyramids, and 288 tetragonal disphenoids of two kinds. 2 dodecagonal prisms, 4 tetragonal dispheonids, and 5 rectangular pyraids join at each vertex. However, it cannot be made scaliform.

It can be formed as the convex hull of 2 oppositely oriented semi-uniform dodecagonal duoprisms where the larger dodecagon is more than $\sqrt6-\sqrt2$ times the edge length of the smaller one.