Metabigyrate rhombicosidodecahedron: Difference between revisions
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{{Short description|74th Johnson solid}} |
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{{Infobox_Polyhedron | |
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{{Infobox polyhedron |
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|image=metabigyrate_rhombicosidodecahedron.png |
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Polyhedron_Type=[[Johnson solid|Johnson]] | |
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|type=[[Johnson solid|Johnson]]<br>{{math|[[parabigyrate rhombicosidodecahedron|''J''{{sub|73}}]] – '''''J''{{sub|74}}''' – [[trigyrate rhombicosidodecahedron|''J''{{sub|75}}]]}} |
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Face_List=20 triangles <br> 30 squares <br> 12 pentagons | |
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|faces=4x2+3x4 [[triangle]]s <br> 2+2x2+6x4 [[square (geometry)|squares]] <br> 4x2+4 [[pentagon]]s |
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Edge_Count=120 | |
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|edges=120 |
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Vertex_Count=60 | |
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|vertices=60 |
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Symmetry_Group=-| |
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|symmetry={{math|''C''{{sub|2v}}}} |
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Vertex_List=-| |
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|vertex_config={{math|5.4(3.4{{sup|2}}.5)<br>4x2+8x4(3.4.5.4)}} |
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Dual=-| |
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|dual=- |
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Property_List=[[convex]]}} |
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|properties=[[convex polytope|convex]], [[Midsphere#Canonical_polyhedron|canonical]] |
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|net=Johnson solid 74 net.png |
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}} |
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In [[geometry]], the '''metabigyrate rhombicosidodecahedron''' is one of the [[Johnson solid]]s ( |
In [[geometry]], the '''metabigyrate rhombicosidodecahedron''' is one of the [[Johnson solid]]s ({{math|''J''{{sub|74}}}}). It can be constructed as a [[rhombicosidodecahedron]] with two non-opposing [[pentagonal cupola]]e rotated through 36 degrees. It is also a [[Midsphere#Canonical polyhedron|canonical polyhedron]]. |
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{{Johnson solid}} |
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Alternative Johnson solids, constructed by rotating different cupolae of a rhombicosidodecahedron, are: |
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* The [[gyrate rhombicosidodecahedron]] ({{math|''J''{{sub|72}}}}) where only one cupola is rotated; |
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* The [[parabigyrate rhombicosidodecahedron]] ({{math|''J''{{sub|73}}}}) where two opposing cupolae are rotated; |
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* And the [[trigyrate rhombicosidodecahedron]] ({{math|''J''{{sub|75}}}}) where three cupolae are rotated. |
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==External links== |
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* {{Mathworld2 | urlname2 = JohnsonSolid | title2 = Johnson solid | urlname =MetabigyrateRhombicosidodecahedron | title = Metabigyrate rhombicosidodecahedron }} |
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*[https://web.archive.org/web/20051215163324/http://www.viviasoft.com/polyhedra/convex/johnson/169_j74.htm World of Polyhedra - metabigyrate rhombicosidodecahedron] (interactive rotatable wireframe applet) |
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[[Category:Johnson solids]] |
[[Category:Johnson solids]] |
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{{Johnson solids navigator}} |
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Latest revision as of 21:06, 14 June 2022
| Metabigyrate rhombicosidodecahedron | |
|---|---|
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| Type | Johnson J73 – J74 – J75 |
| Faces | 4x2+3x4 triangles 2+2x2+6x4 squares 4x2+4 pentagons |
| Edges | 120 |
| Vertices | 60 |
| Vertex configuration | 5.4(3.42.5) 4x2+8x4(3.4.5.4) |
| Symmetry group | C2v |
| Dual polyhedron | - |
| Properties | convex, canonical |
| Net | |
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In geometry, the metabigyrate rhombicosidodecahedron is one of the Johnson solids (J74). It can be constructed as a rhombicosidodecahedron with two non-opposing pentagonal cupolae rotated through 36 degrees. It is also a canonical polyhedron.
A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra (that is, they are not Platonic solids, Archimedean solids, prisms, or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.[1]
Alternative Johnson solids, constructed by rotating different cupolae of a rhombicosidodecahedron, are:
- The gyrate rhombicosidodecahedron (J72) where only one cupola is rotated;
- The parabigyrate rhombicosidodecahedron (J73) where two opposing cupolae are rotated;
- And the trigyrate rhombicosidodecahedron (J75) where three cupolae are rotated.
External links
[edit]- Weisstein, Eric W., "Metabigyrate rhombicosidodecahedron" ("Johnson solid") at MathWorld.
- World of Polyhedra - metabigyrate rhombicosidodecahedron (interactive rotatable wireframe applet)
 | This polyhedron-related article is a stub. You can help Wikipedia by expanding it. |
- ^ Johnson, Norman W. (1966), "Convex polyhedra with regular faces", Canadian Journal of Mathematics, 18: 169–200, doi:10.4153/cjm-1966-021-8, MR 0185507, Zbl 0132.14603.