Rectified grand hexacosichoron

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Rectified grand hexacosichoron
Rank4
TypeUniform
Notation
Bowers style acronymRaggix
Coxeter diagramo5/2o3x3o ()
Elements
Cells
Faces1200+2400 triangles
Edges3600
Vertices720
Vertex figurePentagrammic prism, edge length 1
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {5-2{\sqrt {5}}}}\approx 0.72654}$
Hypervolume${\displaystyle 25{\frac {15{\sqrt {5}}-31}{4}}\approx 15.88137}$
Dichoral anglesGike–3–oct: ${\displaystyle \arccos \left(-{\frac {\sqrt {7-3{\sqrt {5}}}}{4}}\right)\approx 97.76124^{\circ }}$
Oct–3–oct: ${\displaystyle \arccos \left({\frac {3{\sqrt {5}}-1}{8}}\right)\approx 44.47751^{\circ }}$
Central density191
Number of external pieces73440
Level of complexity272
Related polytopes
ArmyRox
RegimentRigfix
ConjugateRectified hexacosichoron
Convex coreHexacosichoron
Abstract & topological properties
Flag count43200
Euler characteristic0
OrientableYes
Properties
SymmetryH4, order 14400
Flag orbits3
ConvexNo
NatureTame

The rectified grand hexacosichoron, or raggix, is a nonconvex uniform polychoron that consists of 600 regular octahedra and 120 great icosahedra. Two great icosahedra and 5 octahedra join at each pentagrammic prismatic vertex. As the name suggests, it can be obtained by rectifying the grand hexacosichoron.

Blending 10 rectified grand hexacosichora results in the great disnub dishexacosichoron, which is uniform.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the rectified great faceted hexacosichoron.