Square-hexagonal duoantiprismatic antiprism

Square-hexagonal duoantiprismatic antiprism
File:Square-hexagonal duoantiprismatic antiprism.png (OFF file)
Rank	5
Type	Isogonal
Notation
Bowers style acronym	Shiddapap
Coxeter diagram	s2s8o2s12o
Elements
Tera	96 digonal disphenoidal pyramids, 12 digonal-square duoantiprisms, 8 digonal-hexagonal duoantiprisms, 2 square-hexagonal duoantiprisms
Cells	192+192 sphenoids, 96 rhombic disphenoids, 96 digonal disphenoids, 12+24 square antiprisms, 8+16 hexagonal antiprisms
Faces	384 scalene triangles, 96+96+192+192 isosceles triangles, 24 squares, 16 hexagons
Edges	96+96+96+96+192
Vertices	96
Vertex figure	Disphenoid-gyrobifastigium wedge
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Square-hexagonal duoantitegmatic antitegum
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	(I2(8)×I2(12)×A1)/2, order 384
Convex	Yes
Nature	Tame

The square-hexagonal duoantiprismatic antiprism, or shiddapap, is a convex isogonal polyteron that consists of 2 square-hexagonal duoantiprisms, 8 digonal-hexagonal duoantiprisms, 12 digonal-square duoantiprisms, and 96 digonal disphenoidal pyramids. 1 square-hexagonal duoantiprism, 2 digonal-hexagonal duoantiprisms, 2 digonal-square duoantiprisms, and 5 digonal disphenoidal pyramids join at each vertex. It can be obtained through the process of alternating the octagonal-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:${\sqrt {\frac {66+26{\sqrt {3}}+{\sqrt {1922+1104{\sqrt {3}}}}}{97}}}$ ≈ 1:1.33530.