Hexadecahedral pentacosiheptacontahexachoron

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

Hexadecahedral pentacosiheptacontahexachoron
Rank4
TypeIsotopic
Elements
Cells576 24-vertex hexadecahedra
Faces576+576 scalene triangles, 288+288 kites, 576+576 irregular tetragons, 576 irregular pentagons, 576 irregular hexagons, 288 mirror-symmetric octagons, 288 mirror-symmetric decagons
Edges192+192+576+576+576+576+576+576+576+576+576+576+576+576
Vertices48+144+192+288+288+576+576+576+576
Vertex figure48 tetartoids, 192 chiral triangular antitegums, 144 rhombic disphenoids, 288+288 phyllic disphenoids, 576+576+576+576 irregular tetrahedra
Measures (edge length 1)
Central density1
Related polytopes
DualMedial disphenoidal omnisnub bitetrahedral tetracontoctachoron
Abstract & topological properties
Flag count87552
Euler characteristic0
OrientableYes
Properties
SymmetryA3●B3, order 576
ConvexYes
NatureTame

Each cell of this polychoron is completely asymmetric, with 1 decagon, 1 octagon, 2 hexagons, 2 pentagons, 6 tetragons, and 4 triangles for faces.