Small intercepted ditetrahedronary trishecatonicosachoron

(Redirected from Sand tathi)
Small intercepted ditetrahedronary trishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymSand tathi
Elements
Cells120 dodecahedra, 120 small ditrigonary icosidodecahedra, 120 small dodecicosidodecahedra
Faces2400 triangles, 1440 pentagons, 720 pentagrams, 720 decagons
Edges3600
Vertices600
Measures (edge length 1)
Circumradius${\displaystyle {\frac {{\sqrt {2}}+{\sqrt {10}}}{2}}\approx 2.28825}$
Hypervolume${\displaystyle 5{\frac {605+243{\sqrt {5}}}{4}}\approx 1435.45565}$
Dichoral anglesSidtid–5/2–sidtid: 144°
Central density87
Number of external pieces24120
Level of complexity49
Related polytopes
ArmyHi, edge length ${\displaystyle {\frac {{\sqrt {5}}-1}{2}}}$
RegimentSidtaxhi
ConjugateGrand retroditetrahedronary trishecatonicosachoron
Abstract & topological properties
Flag count100800
Euler characteristic1920
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureWild

The small intercepted ditetrahedronary trishecatonicosachoron, or sand tathi, is a nonconvex uniform polychoron that consists of 120 small ditrigonary icosidodecahedra, 120 dodecahedra, and 120 small dodecicosidodecahedra. Four small ditrigonary icosidodecahedra, four dodecahedra, and twelve small dodecicosidodecahedra join at each vertex.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small ditetrahedronary hexacosihecatonicosachoron.