# Compound of six pentagrammic prisms

Compound of six pentagrammic prisms
Rank3
TypeUniform
Notation
Bowers style acronymGikrid
Elements
Components6 pentagrammic prisms
Faces30 squares, 12 pentagrams
Edges30+60
Vertices60
Vertex figureIsosceles triangle, edge lengths (5–1)/2, 2, 2
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {15-2{\sqrt {5}}}{20}}}\approx 0.72553}$
Volume${\displaystyle {\frac {3{\sqrt {25-10{\sqrt {5}}}}}{2}}\approx 2.43690}$
Dihedral angles4–5/2: 90°
4–4: 36°
Central density12
Number of external pieces192
Level of complexity38
Related polytopes
ArmySrid, edge length ${\displaystyle {\sqrt {\frac {5-2{\sqrt {5}}}{5}}}}$
RegimentGikrid
DualCompound of six pentagrammic tegums
ConjugateCompound of six pentagonal prisms
Convex coreRhombic triacontahedron
Abstract & topological properties
Flag count360
OrientableYes
Properties
SymmetryH3+, order 60
ConvexNo
NatureTame

The great chirorhombidodecahedron, gikrid, or compound of six pentagrammic prisms is a uniform polyhedron compound. It consists of 30 squares and 12 pentagrams, with one pentagram and two squares joining at a vertex.

Its quotient prismatic equivalent is the pentagrammic prismatic hexateroorthowedge, which is eight-dimensional.

## Vertex coordinates

The vertices of a great chirorhombidodecahedron of edge length 1 are given by all permutations of:

• ${\displaystyle \left(\pm {\sqrt {\frac {5+2{\sqrt {5}}}{20}}},\,\pm {\sqrt {\frac {5-2{\sqrt {5}}}{20}}},\,\pm {\sqrt {\frac {5-2{\sqrt {5}}}{20}}}\right)}$,

plus all even permutations of:

• ${\displaystyle \left(0,\,\pm {\sqrt {\frac {5+{\sqrt {5}}}{40}}},\,\pm {\sqrt {\frac {5-{\sqrt {5}}}{8}}}\right)}$,
• ${\displaystyle \left(\pm {\sqrt {\frac {5+{\sqrt {5}}}{40}}},\,\pm {\sqrt {\frac {5-{\sqrt {5}}}{40}}},\,\pm {\sqrt {\frac {5-{\sqrt {5}}}{10}}}\right)}$.

This compound is chiral. The compound of the two enantiomorphs is the great disrhombidodecahedron.