Hexagonal antiditetragoltriate

Hexagonal antiditetragoltriate
(OFF file)
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Hadet
Elements
Cells	36+36 tetragonal disphenoids, 72 rectangular pyramids, 12 hexagonal prisms
Faces	144+144 isosceles triangles, 72 rectangles, 12 hexagons
Edges	72+72+144
Vertices	72
Vertex figure	Biaugmented triangular prism
Measures (based on same duoprisms as optimized hexagonal ditetragoltriate)
Edge lengths	Edges of smaller hexagon (72): 1
	Lacing edges (144): ${\sqrt {5+2{\sqrt {2}}-2{\sqrt {3}}-{\sqrt {6}}}}\approx 1.38378$
	Edges of larger hexagon (72): ${\frac {2+{\sqrt {2}}}{2}}\approx 1.70711$
Circumradius	${\sqrt {\frac {5+2{\sqrt {2}}}{2}}}\approx 1.97844$
Central density	1
Related polytopes
Army	Hadet
Regiment	Hadet
Dual	Hexagonal antitetrambitriate
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	G2≀S2, order 288
Convex	Yes
Nature	Tame

The hexagonal antiditetragoltriate or hadet is a convex isogonal polychoron and the fourth member of the antiditetragoltriate family. It consists of 12 hexagonal prisms, 72 rectangular pyramids, and 72 tetragonal disphenoids of two kinds. 2 hexagonal prisms, 4 tetragonal disphenoids, and 5 rectangular pyramids join at each vertex. However, it cannot be made scaliform.

It can be formed as the convex hull of 2 oppositely oriented semi-uniform hexagonal duoprisms where the larger hexagon is more than ${\frac {2{\sqrt {3}}}{3}}$ times the edge length of the smaller one.