# Small ditrigonary hexacosihecatonicosachoron

(Redirected from Sidtixhi)
Small ditrigonary hexacosihecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymSidtixhi
Coxeter diagramx3o3o3o5/2*b ()
Elements
Cells600 tetrahedra, 120 great icosahedra
Faces2400 triangles
Edges1200
Vertices120
Vertex figureSmall ditrigonary icosidodecahedron, edge length 1
Edge figure(tet 3 gike 3)×3
Measures (edge length 1)
Hypervolume${\displaystyle 25{\frac {2{\sqrt {5}}-1}{4}}\approx 21.70085}$
Dichoral angle${\displaystyle \arccos \left(-{\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 157.76124^{\circ }}$
Central density9
Number of external pieces15840
Level of complexity51
Related polytopes
ArmyEx, edge length ${\displaystyle {\frac {{\sqrt {5}}-1}{2}}}$
RegimentSishi
CompanySidtixhi
DualSmall triambic icosahedral hecatonicosachoron
ConjugateGreat ditrigonary hexacosihecatonicosachoron
Convex coreTruncated hexacosichoron
Abstract & topological properties
Flag count28800
Euler characteristic600
OrientableYes
Properties
SymmetryH4, order 14400
Flag orbits2
ConvexNo
NatureTame

The small ditrigonary hexacosihecatonicosachoron, or sidtixhi, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra and 120 regular great icosahedra. 12 great icosahedra and 20 tetrahedra join at each vertex, with a small ditrigonary icosidodecahedron as the vertex figure.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small stellated hecatonicosachoron.

## Related polychora

The small ditrigonary hexacosihecatonicosachoron has the same edges as the regular small stellated hecatonicosachoron. It shares its face arrangement with the ditrigonary dishecatonicosachoron and the great ditrigonary hexacosihecatonicosachoron. Also sharing this set of faces is the dodecahedronary hexacosichoron, a uniform compound of 25 icositetrachora. Besides these three polychora, there is only one other face-transitive uniform polychoron which is not regular, namely the tesseractihemioctachoron.