Expanded icosidodecahedron

Expanded icosidodecahedron
Schläfli symbol	rr$\begin{Bmatrix} 5 \\ 3 \end{Bmatrix}$ = 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 a 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

• Expanded rhombic triacontahedron
• Rectified rhombicosidodecahedron
• Rectified small rhombicosidodecahedron
• Rhombirhombicosidodecahedron

Expansion

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

Dissection

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.

Related polyhedra

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

• Rhombicosidodecahedron (expanded dodecahedron)
• Truncated rhombicosidodecahedron
• Expanded cuboctahedron

References

1. http://mathworld.wolfram.com/UniformPolyhedron.html

• Coxeter Regular Polytopes, Third edition, (1973), Dover edition, ISBN 0-486-61480-8 (pp. 145–154 Chapter 8: Truncation)
• John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5

External links

• George Hart's Conway interpreter: generates polyhedra in VRML, taking Conway notation as input, VRML model
• Convex Polyhedra containing Golden Rhombi: 2. Expanded RTC ('XRTC') and related polyhedral
• Variations on a Rhombic Theme