Expanded icosidodecahedron
{{Short description|Type of polyhedron}}
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!bgcolor=#e7dcc3 colspan=2|Expanded icosidodecahedron | |
| colspan=2 align=center|240px | |
| bgcolor=#e7dcc3|Schläfli symbol | rr = rrr{5,3} |
| bgcolor=#e7dcc3|Conway notation | edaD = aaaD |
| bgcolor=#e7dcc3|Faces | 122: 20 {3} 60 {4} 12 {5} 30 rhombs |
| bgcolor=#e7dcc3|Edges | 240 |
| bgcolor=#e7dcc3|Vertices | 120 |
| bgcolor=#e7dcc3|Symmetry group | Ih, [5,3], (*532) order 120 |
| bgcolor=#e7dcc3|Rotation group | I, [5,3]+, (532), order 60 |
| bgcolor=#e7dcc3|Dual polyhedron | Deltoidal hecatonicosahedron |
| bgcolor=#e7dcc3|Properties | convex |
| colspan=2 align=center|280px 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
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!Name !Expanded |
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!Coxeter{{Cite web|url=http://mathworld.wolfram.com/UniformPolyhedron.html|title=Uniform Polyhedron}} !rowspan=2|D !ID !rID !rrID |
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!aD !aaD = eD !aaaD = eaD |
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!Image |
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!Conway !dD = I !daD = jD !deD = oD !deaD = oaD |
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!Dual |
See also
- Rhombicosidodecahedron (expanded dodecahedron)
- Truncated rhombicosidodecahedron
- Expanded cuboctahedron
References
{{reflist}}
- 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
- [http://www.georgehart.com/virtual-polyhedra/conway_notation.html George Hart's Conway interpreter]: generates polyhedra in VRML, taking Conway notation as input, [http://georgehart.com/virtual-polyhedra/vrml/zonish-6-icosidodecahedron.wrl] VRML model
- [http://www.orchidpalms.com/polyhedra/rhombic/RTC/RTC.htm#XRTC Convex Polyhedra containing Golden Rhombi: 2. Expanded RTC ('XRTC') and related polyhedral]
- [http://www.orchidpalms.com/polyhedra/rhombic/RTC/rhomvar.htm Variations on a Rhombic Theme]