Snub tesseractic antiprism

Snub tesseractic antiprism
File:Snub tesseractic antiprism.png (OFF file)
Rank	5
Type	Isogonal
Notation
Bowers style acronym	Snettap
Coxeter diagram	s2s4s3s3s
Elements
Tera	384 irregular pentachora, 32 digonal-triangular duoantiprisms, 24 digonal-square duoantiprisms, 16 snub tetrahedral antiprisms, 8 snub cubic antiprisms, 2 snub tesseracts
Cells	384+384+384+384+384 irregular tetrahedra, 96+96+96 rhombic disphenoids, 64+64+64 triangular gyroprisms, 48+48 square gyroprisms, 32 snub tetrahedra, 16 snub cubes
Faces	384+384+384+384+384+384+384+384+384+384 scalene triangles, 128+128 triangles, 96 squares
Edges	192+192+192+192+192+192+192+384+384+384
Vertices	384
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Enneahedral hecatonenneacontadichoric antitegum
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	(B4×A1)+, order 384
Convex	Yes
Nature	Tame

The snub tesseractic antiprism or snettap is a convex isogonal polyteron that consists of 2 snub tesseracts, 8 snub cubic antiprisms, 16 snub tetrahedral antiprisms, 24 digonal-square duoantiprisms, 32 digonal-triangular duoantiprisms, and 384 irregular pentachora. 5 pentachora and one of each of the other cell types join at each vertex. It can be obtained through the process of alternating the great disprismatotesseractihexadecachoric prism. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:a ≈ 1:1.25002, where a is the largest real root of 5329x¹²-23652x¹⁰+41382x⁸-37052x⁶+18052x⁴-4560x²+468.

Vertex coordinates

Vertex coordinates for a snub tesseractic antiprism, assuming that the edge length differences are minimized, using the ratio method, are given by all even permutations with an even number of sign changes, plus all odd permutations with an odd amount of sign changes except the last coordinate of:

• $\left(c_{1},\,c_{2},\,c_{3},\,c_{4},\,c_{5}\right),$
• $\left(c_{2},\,c_{1},\,c_{3},\,c_{4},\,-c_{5}\right),$

where

• $c_{1}\approx 0.3191085335012948850450705,$
• $c_{2}\approx 0.6310069285250780509169974,$
• $c_{3}\approx 0.9720792302282349822564494,$
• $c_{4}\approx 1.4440010653634313903563943,$
• $c_{5}\approx 0.3336991298140972819894887.$