Swirlprismatodiminished rectified hexacosichoron

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Swirlprismatodiminished rectified hexacosichoron
Rank4
TypeScaliform
Notation
Bowers style acronymSpidrox
Elements
Cells600 square pyramids, 120 pentagonal prisms, 120 pentagonal antiprisms
Faces600+1200 triangles, 600 squares, 240 pentagons
Edges600+600+1200
Vertices600
Vertex figureParabidiminished pentagonal prism, edge lengths 1, 2, and (1+5)/2
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesPip–4–squippy:
 Squippy–3–squippy:
 Pap–5–pip: 162°
 Pap–3–squippy:
Central density1
Related polytopes
ArmySpidrox
RegimentSpidrox
DualSwirlprismatostellated joined hecatonicosachoron
ConjugateSwirlprismatoreplenished rectified grand hexacosichoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryH3●I2(10), order 1200
ConvexYes
NatureTame

The swirlprismatodiminished rectified hexacosichoron or spidrox, also known as the prismantiprismoidal transitional didecafold icosidodecaswirlchoron, is a convex scaliform polychoron. It consists of 120 pentagonal prisms, 120 pentagonal antiprisms, and 600 square pyramids. 2 pentagonal antiprisms, 2 pentagonal prisms, and 5 square pyramids join at each vertex.

It can be constructed by diminishing the rectified hexacosichoron, specifically by removing the 120 vertices of an inscribed hexacosichoron. As a result every icosahedral cell of the rectified hexacosichoron gets diminished down to a pentagonal antiprism, while every octahedral cell gets diminished down to a square pyramid. The pentagonal prism cells are the vertex figures under the removed vertices.

Vertex coordinates[edit | edit source]

A swirlprismatodiminished rectified hexacosichoron of edge length 1 has vertex coordinates given by:

These are derived by removing 120 vertices from the rectified hexacosichoron.

External links[edit | edit source]