Snub bitetrahedral tetracontoctachoron

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Snub bitetrahedral tetracontoctachoron
File:Snub bitetrahedral tetracontoctachoron.png
Rank4
TypeIsogonal
Notation
Bowers style acronymSebtic
Elements
Cells288 phyllic disphenoids, 192 chiral triangular antipodiums, 48 snub tetrahedra
Faces576+576 scalene triangles, 288 isosceles triangles, 192+192 triangles
Edges144+288+576+576
Vertices288
Vertex figure11-vertex polyhedron with 2 pentagons, 4 tetragons, and 4 triangles
Measures (edge length 1)
Central density1
Related polytopes
ArmySebtic
RegimentSebtic
DualHendecahedral diacosioctacontoctachoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryA3●B3, order 576
ConvexYes
NatureTame

The snub bitetrahedral tetracontoctachoron or sebtic is a convex isogonal polychoron that consists of 48 snub tetrahedra, 192 chiral triangular antipodiums and 288 phyllic disphenoids. 2 snub tetrahedra, 4 chiral triangular antipodiums, and 4 phyllic disphenoids join at each vertex. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.48563.

Vertex coordinates[edit | edit source]

Vertex coordinates for a snub bitetrahedral tetracontoctachoron, assuming that the edge length differences are minimized, are given by all even permutations with an even number of sign changes of:

as well as all even permutations with an odd number of sign changes of:

Another set of coordinates for a snub bitetrahedral tetracontoctachoron, assuming that the ratio method is used, are given by all even permutations with an even number of sign changes of:

as well as all even permutations with an odd number of sign changes of: