Intercepted invertipental hexacosidishecatonicosachoron

Intercepted invertipental hexacosidishecatonicosachoron
Rank4
TypeUniform
Notation
Elements
Cells
Faces
Edges3600
Vertices720
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {5+2{\sqrt {5}}}}\approx 3.07768}$
Hypervolume${\displaystyle 5{\frac {1245+557{\sqrt {5}}}{4}}\approx 3113.11233}$
Dichoral anglesOct–3–oct: ${\displaystyle \arccos \left(-{\frac {1+3{\sqrt {5}}}{8}}\right)\approx 164.47751^{\circ }}$
Srid–4–srid: 90°
Oct–3–srid: ${\displaystyle \arccos \left(-{\frac {\sqrt {10}}{4}}\right)\approx 37.76124^{\circ }}$
Number of external pieces17520
Level of complexity33
Related polytopes
ArmyRox
RegimentRox
ConjugateCircumfacetopental hexacosidishecatonicosachoron
Convex coreHecatonicosachoron
Abstract & topological properties
Flag count100800
Euler characteristic3120
OrientableYes
Properties
SymmetryH4, order 14400
Flag orbits7
ConvexNo
NatureWild

The intercepted invertipental hexacosidishecatonicosachoron, or nipixady, is a nonconvex uniform polychoron that consists of 120 great dodecahedra, 120 small rhombicosidodecahedra, and 600 octahedra. 2 great dodecahedra, 5 octahedra, and 10 small rhombicosidodecahedra join at each vertex.

It is superficially identical to the invertopental hexacosidishecatonicosachoron, differing only internally.

Vertex coordinates

The vertices are the same as those of its regiment colonel, the rectified hexacosichoron.