释义 |
- Other names
- Expansion
- Dissection
- Related polyhedra
- See also
- References
- External links
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 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 |
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Conway | 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 |
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See also - Rhombicosidodecahedron (expanded dodecahedron)
- Truncated rhombicosidodecahedron
- Expanded cuboctahedron
References1. ^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
1 : Polyhedra |