Truncated dodecagonal duoprism

Truncated dodecagonal duoprism
(OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Notation
Bowers style acronym	Tatwaddip
Elements
Cells	144 tetragonal disphenoids, 24 truncated dodecagonal prisms
Faces	576 isosceles triangles, 144 ditetragons, 24 didodecagons
Edges	288+288+576
Vertices	576
Vertex figure	Sphenoid
Measures (based on icositetragon edge length 1)
Edge lengths	Lacing edges (576): $\sqrt3-1 ≈ 0.73205$
	Edges of icositetragons (288+288): 1
Circumradius	$\sqrt{\frac{20+9\sqrt2+6\sqrt3+7\sqrt6}{2}} ≈ 5.48938$
Central density	1
Related polytopes
Army	Tatwaddip
Regiment	Tatwaddip
Dual	Tetrakis dodecagonal duotegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(12)≀S2, order 1152
Convex	Yes
Nature	Tame

The truncated dodecagonal duoprism or tatwaddip is a convex isogonal polychoron that consists of 24 truncated dodecagonal prisms and 144 tetragonal disphenoids. 1 tetragonal disphenoid and 3 truncated dodecagonal prisms join at each vertex. It can be formed by truncating the dodecagonal duoprism.

It can also be obtained as the convex hull of 2 semi-uniform dodecagonal-icositetragonal duoprisms chosen such that the icositetragonal and dodecagonal prisms have the same circumradius. if the icositetragons of this duoprism have edge length 1, the dodecagons have edge length $1-\sqrt2+\sqrt6 ≈ 2.03528$.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$\frac{1+\sqrt3}{2}$ ≈ 1:1.36603.