Snub tetracontoctachoric antiprism

Snub tetracontoctachoric antiprism
File:Snub tetracontoctachoric antiprism.png (OFF file)
Rank	5
Type	Isogonal
Notation
Bowers style acronym	Snocap
Coxeter diagram	s2s3s4s3s
Elements
Tera	1152 phyllic disphenoidal pyramids, 192 digonal-triangular duoantiprisms, 48 snub cubic antiprisms, 2 snub tetracontoctachora
Cells	2304+2304 irregular tetrahedra, 1152 phyllic disphenoids, 576 rhombic disphenoids, 288 tetragonal disphenoids, 384+384 triangular gyroprisms, 144 square antiprisms, 96 snub cubes
Faces	2304+2304+2304+2304 scalene triangles, 1152+1152 isosceles triangles, 768 triangles, 288 squares
Edges	576+1152+1152+1152+1152+2304
Vertices	1152
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Enneahedral pentacosiheptacontahexachoric antitegum
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	(F4×2×A1)+, order 2304
Convex	Yes
Nature	Tame

The snub tetracontoctachoric antiprism or snocap, also commonly called the omnisnub icositetrachoric antiprism, is a convex isogonal polyteron that consists of 2 snub tetracontoctachora, 48 snub cubic antiprisms, 192 digonal-triangular duoantiprisms, and 1152 phyllic disphenoidal pyramids. 1 snub tetracontoctachoron, 2 snub cubic antiprisms, 2 digonal-triangular duoantiprisms, and 5 phyllic dispehnoidal pyramids join at each vertex. It can be obtained through the process of alternating the great prismatotetracontoctachoric prism. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:${\frac {\sqrt {4+2{\sqrt {2{\sqrt {2}}-2}}}}{2}}$ ≈ 1:1.20627.