# Small hexacosihecatonicosihecatonicosachoron

Small hexacosihecatonicosihecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymSixhihy
Coxeter diagramo3o3/2x5x5*b ()
Elements
Cells600 tetrahedra, 120 dodecahedra, 120 small dodecicosidodecahedra
Faces2400 triangles, 1440 pentagons, 720 decagons
Edges3600+3600
Vertices2400
Vertex figureCrossed triangular frustum, edge lengths 1 (small base), (1+5)/2 (large base), and (5+5)/2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle 3+{\sqrt {5}}\approx 5.23607}$
Hypervolume$\displaystyle 5\frac{3665+1622\sqrt5}{4} \approx 9114.87782$
Saddid–3–tet: ${\displaystyle \arccos \left({\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 22.23876^{\circ }}$
Number of external pieces4560
Level of complexity12
Related polytopes
ArmySidpixhi
RegimentSidpixhi
ConjugateGreat hexacosihecatonicosihecatonicosachoron
Abstract & topological properties
Flag count86400
Euler characteristic–1080
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The small hexacosihecatonicosihecatonicosachoron, or sixhihy, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 regular dodecahedra, and 120 small dodecicosidodecahedra. 1 tetrahedron, 1 dodecahedron, and 3 small dodecicosidodecahedra join at each vertex.

## Vertex coordinates

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