Rank3
TypeUniform
SpaceSpherical
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${\displaystyle \frac{\sqrt7}{2} \approx 1.32288}$
Volume20
Dihedral angles5–6: ${\displaystyle \arccos\left(\sqrt{\frac{5-2\sqrt5}{15}}\right) \approx 79.18768^\circ}$
5/2–6: ${\displaystyle \arccos\left(\sqrt{\frac{5+2\sqrt5}{15}}\right) \approx 37.37737^\circ}$
Central density4
Number of external pieces408
Level of complexity25
Related polytopes
ArmySemi-uniform ti, edge lengths ${\displaystyle \frac{\sqrt5-1}{2}}$ (pentagons), ${\displaystyle \frac{3-\sqrt5}{2}}$ (between ditrigons)
DualMedial icosacronic hexecontahedron
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

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

## Related polyhedra

o5/3o3o5*a truncations
Name OBSA CD diagram Picture