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	I_h, [5,3], (*532) order 120
Rotation group	I, [5,3]⁺, (532), order 60
Dual polyhedron
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[]

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	D	aD	aaD = eD	aaaD = eaD
Image
Conway	dD = I	daD = jD	deD = oD	deaD = oaD
Dual

References[]

^ "Uniform Polyhedron".

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, [1] VRML model
Convex Polyhedra containing Golden Rhombi: 2. Expanded RTC ('XRTC') and related polyhedral
Variations on a Rhombic Theme

[1] "Uniform Polyhedron".

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