Great hexacosifaceted trishecatonicosachoron

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Great hexacosifaceted trishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymGaxifthi
Elements
Cells120 dodecahedra, 120 quasitruncated great stellated dodecahedra, 120 great ditrigonal dodecicosidodecahedra
Faces2400 triangles, 1440 pentagons, 1440 decagrams
Edges3600+3600
Vertices2400
Vertex figureTriangular hemiantipodium, edge lengths (1+5)/2 (top triangle), 1 (base pseudo-triangle), and (5–5)/2 (sides)
Measures (edge length 1)
Circumradius
Dichoral anglesGidditdid–3–quit gissid: 120°
 Gidditdid–10/3–quit gissid: 108°
 Gidditdid–5–doe: 72°
Number of external pieces57960
Level of complexity184
Related polytopes
ArmySemi-uniform Sidpixhi
RegimentGixhidy
ConjugateSmall hexacosifaceted trishecatonicosachoron
Abstract & topological properties
Euler characteristic120
OrientableNo
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The great hexacosifaceted trishecatonicosachoron, or gaxifthi, is a nonconvex uniform polychoron that consists of 120 dodecahedra, 120 quasitruncated great stellated dodecahedra, and 120 great ditrigonal dodecicosidodecahedra. One dodecahedron, three quasitruncated great stellated dodecahedra, and three great ditrigonal dodecicosidodecahedra join at each vertex.

It also has 600 tetrahedra and 120 quasitruncated small stellated dodecahedra as pseudofacets.

Gallery[edit | edit source]

Card with cell counts, vertex figure, and cross-sections.


Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the great hexacosihecatonicosidishecatonicosachoron.

External links[edit | edit source]