Compound of six pentagrammic prisms

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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
Volume
Dihedral angles4–5/2: 90°
 4–4: 36°
Central density12
Number of external pieces192
Level of complexity38
Related polytopes
ArmySrid, edge length
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[edit | edit source]

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

  • ,

plus all even permutations of:

  • ,
  • .

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

External links[edit | edit source]