Truncated hexagonal duoprism

Truncated hexagonal duoprism
(OFF file)
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Tahiddip
Elements
Cells	36 tetragonal disphenoids, 12 truncated hexagonal prisms
Faces	144 isosceles triangles, 36 ditetragons, 12 dihexagons
Edges	72+72+144
Vertices	144
Vertex figure	Sphenoid
Measures (variant with dodecagon edge length 1)
Edge lengths	Lacing edges (144): ${\frac {\sqrt {6}}{3}}\approx 0.81650$
	Edges of dodecagons (72+72): 1
Circumradius	${\sqrt {\frac {13+7{\sqrt {3}}}{3}}}\approx 2.89392$
Central density	1
Related polytopes
Army	Tahiddip
Regiment	Tahiddip
Dual	Tetrakis hexagonal duotegum
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	G2≀S2, order 288
Convex	Yes
Nature	Tame

The truncated hexagonal duoprism or tahiddip is a convex isogonal polychoron that consists of 12 truncated hexagonal prisms and 36 tetragonal disphenoids. 1 tetragonal disphenoid and 3 truncated hexagonal prisms join at each vertex. It can be formed by truncating the hexagonal duoprism.

It can also be obtained as the convex hull of 2 semi-uniform hexagonal-dodecagonal duoprisms chosen such that the dodecagonal and hexagonal prisms have the same circumradius. if the dodecagons of this duoprism have edge length 1, the hexagons have edge length ${\frac {3+2{\sqrt {3}}}{3}}\approx 2.15470$.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is ${\frac {\sqrt {6}}{2}}\approx 1.22474$.