Icosidodecadodecahedron

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Icosidodecadodecahedron
Rank3
TypeUniform
Notation
Bowers style acronymIded
Coxeter diagramo5/3x3x5*a ()
Elements
Faces12 pentagons, 12 pentagrams, 20 hexagons
Edges60+60
Vertices60
Vertex figureCrossed isosceles trapezoid, edge lengths (5–1)/2, 3, (1+5)/2, 3
Measures (edge length 1)
Circumradius
Volume20
Dihedral angles5–6:
 5/2–6:
Central density4
Number of external pieces408
Level of complexity25
Related polytopes
ArmySemi-uniform ti, edge lengths (pentagons), (between ditrigons)
RegimentRaded
DualMedial icosacronic hexecontahedron
ConjugateIcosidodecadodecahedron
Convex coreTruncated icosahedron
Abstract & topological properties
Flag count480
Euler characteristic–16
OrientableYes
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The icosidodecadodecahedron, or ided, is a uniform polyhedron. It consists of 12 pentagons, 12 pentagrams, and 20 hexagons. One pentagon, one pentagram, and two hexagons join at each vertex.

It is a faceting of the rhombidodecadodecahedron, using its 12 pentagrams and 12 pentagons along with 20 additional hexagons.

Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the rhombidodecadodecahedron.

Related polyhedra[edit | edit source]

o5/3o3o5*a truncations
Name OBSA CD diagram Picture
Ditrigonary dodecadodecahedron ditdid
Small complex icosidodecahedron (degenerate, ike+gad) cid
Great complex icosidodecahedron (degenerate, sissid+gike) gacid
Icosidodecadodecahedron ided
Small ditrigonal dodecicosidodecahedron sidditdid
Great ditrigonal dodecicosidodecahedron gidditdid
Icosidodecatruncated icosidodecahedron idtid
Snub icosidodecadodecahedron sided


External links[edit | edit source]