Small dodecahedral pentacosiheptacontahexachoron

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Small dodecahedral pentacosiheptacontahexachoron
Rank4
TypeIsotopic
Elements
Cells576 14-vertex dodecahedra
Faces576+576 scalene triangles, 288+288+288 kites, 576 irregular tetragons, 576 irregular pentagons, 288 mirror-symmetric hexagons
Edges192+192+192+576+576+576+576+576+576+576
Vertices48+144+192+192+288+288+576
Vertex figure48 tetartoids, 192+192 chiral triangular antitegums, 144 rhombic disphenoids, 288+288 phyllic disphenoids, 576 irregular tetrahedra
Measures (edge length 1)
Central density1
Related polytopes
DualSmall omnisnub bitetrahedral tetracontoctachoron
Abstract & topological properties
Flag count55296
Euler characteristic0
OrientableYes
Properties
SymmetryA3●B3, order 576
ConvexYes
NatureTame

The small dodecahedral pentacosiheptacontahexachoron is a convex isochoric polychoron with 576 identical cells. It can be obtained as the dual of the small omnisnub bitetrahedral tetracontoctachoron.

Each cell of this polychoron is completely asymmetric, with 1 hexagon, 2 pentagons, 5 tetragons, and 4 triangles for faces.