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.

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

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