Compound of two great inverted retrosnub icosidodecahedra

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Compound of two great inverted retrosnub icosidodecahedra
Rank3
TypeUniform
Notation
Bowers style acronymGidrissid
Elements
Components2 great inverted retrosnub icosidodecahedra
Faces120 triangles, 40 triangles as 20 hexagrams, 24 pentagrams as 12 stellated decagrams
Edges60+120+120
Vertices120
Vertex figureIrregular pentagram, edge lengths 1, 1, 1, 1, (5–1)/2
Measures (edge length 1)
Circumradius≈ 0.58000
Volume≈ 2.07520
Dihedral angles5/2–3: ≈ 67.31029°
 3–3: ≈ 21.72466°
Central density74
Number of external pieces2580
Related polytopes
ArmySemi-uniform Grid
RegimentGidrissid
DualCompound of two great pentagrammic hexecontahedra
ConjugatesCompound of two snub dodecahedra, compound of two great snub icosidodecahedra, compound of two great inverted snub icosidodecahedra
Convex coreOrder-6-truncated disdyakis triacontahedron
Abstract & topological properties
OrientableYes
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The great diretrosnub icosidodecahedron, gidrissid, or compound of two great inverted retrosnub icosidodecahedra is a uniform polyhedron compound. It consists of 120 snub triangles, 40 further triangles, and 24 pentagrams (the latter two can combine in pairs due to faces in the same plane). Four triangles and one pentagram join at each vertex.

Its quotient prismatic equivalent is the great inverted retrosnub icosidodecahedral antiprism, which is four-dimensional.

Measures[edit | edit source]

The circumradius of the great diretrosnub icosidodecahedron with unit edge length is the smallest positive real root of:

Its volume is given by the smallest positive real root of:

External links[edit | edit source]