Hexagonal duoantiprismatic antiprism

Hexagonal duoantiprismatic antiprism
File:Hexagonal duoantiprismatic antiprism.png (OFF file)
Rank	5
Type	Isogonal
Notation
Bowers style acronym	Hiddapap
Coxeter diagram	s2s12o2s12o
Elements
Tera	144 tetragonal disphenoidal pyramids, 24 digonal-hexagonal duoantiprisms, 2 hexagonal duoantiprisms
Cells	576 sphenoids, 144+144 tetragonal disphenoids, 24+48 hexagonal antiprisms
Faces	288+576+576 isosceles triangles, 48 hexagons
Edges	288+288+288
Vertices	144
Vertex figure	Disphenoid-gyrobifastigium wedge
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Hexagonal duoantitegmatic antitegum
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	(I2(12)≀S2×A1)/2, order 1152
Convex	Yes
Nature	Tame

The hexagonal duoantiprismatic antiprism, or hiddapap, is a convex isogonal polyteron that consists of 2 hexagonal duoantiprisms, 24 digonal-hexagonal duoantiprisms, and 144 tetragonal disphenoidal pyramids. 1 hexagonal duoantiprism, 4 digonal-hexagonal duoantiprisms, and 5 tetragonal disphenoidal pyramids join at each vertex. It can be obtained through the process of alternating the dodecagonal duoprismatic prism. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is $1:{\frac {1+{\sqrt {3}}}{2}}\approx 1:1.36603$.