Expanded icosidodecahedron

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.

Expanded icosidodecahedron
Schläfli symbolrr = rrr{5,3}
Conway notationedaD = aaaD
Faces122:
20 {3}
60 {4}
12 {5}
30 rhombs
Edges240
Vertices120
Symmetry groupIh, [5,3], (*532) order 120
Rotation groupI, [5,3]+, (532), order 60
Dual polyhedronDeltoidal hecatonicosahedron
Propertiesconvex

Net

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.

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

References

  • 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
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.