Great dodecahedral pentacosiheptacontahexachoron

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

Great dodecahedral pentacosiheptacontahexachoron
Rank4
TypeIsotopic
Elements
Cells576 17-vertex dodecahedra
Faces288+288+288 kites, 576+576 irregular tetragons, 576+576 irregular pentagons, 288 mirror-symmetric hexagons
Edges192+192+576+576+576+576+576+576+576+576
Vertices48+144+192+288+288+576+576
Vertex figure48 tetartoids, 192 chiral triangular antitegums, 576 skew kite pyramids, 144 rhombic disphenoids, 288+288 phyllic disphenoids, 576 irregular tetrahedra
Measures (edge length 1)
Central density1
Related polytopes
DualGreat omnisnub bitetrahedral tetracontoctachoron
Abstract & topological properties
Flag count62208
Euler characteristic0
OrientableYes
Properties
SymmetryA3●B3, order 576
ConvexYes
NatureTame

Each cell of this polychoron is completely asymmetric, with 1 hexagon, 4 pentagons, and 7 tetragons for faces.