Jump to content

Expanded icosidodecahedron

From Wikipedia, the free encyclopedia
Expanded icosidodecahedron
Schläfli symbol rr = rrr{5,3}
Conway notation edaD = aaaD
Faces 122:
20 {3}
60 {4}
12 {5}
30 rhombs
Edges 240
Vertices 120
Symmetry group Ih, [5,3], (*532) order 120
Rotation group I, [5,3]+, (532), order 60
Dual polyhedron Deltoidal hecatonicosahedron
Properties convex

Net

The expanded icosidodecahedron is a polyhedron, constructed as an expanded icosidodecahedron. It has 122 faces: 20 triangles, 60 squares, 12 pentagons, and 30 rhombs. The 120 vertices exist at two sets of 60, with a slightly different distance from its center.

It can also be constructed as a rectified rhombicosidodecahedron.

Other names

[edit]
  • Expanded rhombic triacontahedron
  • Rectified rhombicosidodecahedron
  • Rectified small rhombicosidodecahedron
  • Rhombirhombicosidodecahedron

Expansion

[edit]

The expansion operation from the rhombic triacontahedron can be seen in this animation:

Dissection

[edit]

This polyhedron can be dissected into a central rhombic triacontahedron surrounded by: 30 rhombic prisms, 20 tetrahedra, 12 pentagonal pyramids, 60 triangular prisms.

If the central rhombic triacontahedron and the 30 rhombic prisms are removed, you can create a toroidal polyhedron with all regular polygon faces.

[edit]
Name Dodeca-
hedron
Icosidodeca-
hedron
Rhomb-
icosidodeca-
hedron
Expanded
icosidodeca-
hedron
Coxeter[1] D ID rID rrID
Conway aD aaD = eD aaaD = eaD
Image
Conway dD = I daD = jD deD = oD deaD = oaD
Dual

See also

[edit]

References

[edit]
  1. ^ "Uniform Polyhedron".
[edit]