Great icosicosidodecahedron: Difference between revisions
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{{Short description|Polyhedron with 52 faces}} |
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{{Uniform polyhedra db|Uniform polyhedron stat table|gIID}} |
{{Uniform polyhedra db|Uniform polyhedron stat table|gIID}} |
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[[File:Great icosicosidodecahedron.stl|thumb|3D model of a great icosicosidodecahedron]] |
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In [[geometry]], the '''great icosicosidodecahedron''' is a nonconvex [[uniform polyhedron]], indexed as U<sub>48</sub>. |
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In [[geometry]], the '''great icosicosidodecahedron''' (or '''great icosified icosidodecahedron''') is a [[nonconvex uniform polyhedron]], indexed as U<sub>48</sub>. It has 52 faces (20 [[Triangle|triangles]], 12 [[Pentagon|pentagons]], and 20 [[Hexagon|hexagons]]), 120 edges, and 60 vertices.<ref>{{Cite web|url=https://www.mathconsult.ch/enwiki/static/unipoly/48.html|title=48: great icosicosidodecahedron|last=Maeder|first=Roman|date=|website=MathConsult|archive-url=|archive-date=|access-date=}}</ref> Its [[vertex figure]] is a [[quadrilateral#More quadrilaterals|crossed quadrilateral]]. |
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== Related polyhedra == |
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| ⚫ | It shares its [[vertex arrangement]] with the [[truncated dodecahedron]]. It additionally shares its [[edge arrangement]] with the [[great ditrigonal dodecicosidodecahedron]] (having the triangular and pentagonal faces in common) and the [[great dodecicosahedron]] (having the hexagonal faces in common). |
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{| class="wikitable" width="400" style="vertical-align:top;text-align:center" |
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| [[Image:Truncated dodecahedron.png|100px]]<BR>[[Truncated dodecahedron]] |
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| [[Image:Great icosicosidodecahedron.png|100px]]<BR>'''Great icosicosidodecahedron''' |
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| [[Image:Great ditrigonal dodecicosidodecahedron.png|100px]]<BR>[[Great ditrigonal dodecicosidodecahedron]] |
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| [[Image:Great dodecicosahedron.png|100px]]<BR>[[Great dodecicosahedron]] |
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|} |
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== References == |
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{{Reflist}} |
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== External links == |
== External links == |
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* {{mathworld2 | urlname = GreatIcosicosidodecahedron| title = Great icosicosidodecahedron | urlname2 = UniformPolyhedron| title2 = Uniform polyhedron}} |
* {{mathworld2 | urlname = GreatIcosicosidodecahedron| title = Great icosicosidodecahedron | urlname2 = UniformPolyhedron| title2 = Uniform polyhedron}} |
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[[Category:Uniform polyhedra]] |
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[[eo:Granda dudek-dudek-dekduedro]] |
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[[fr:Grand icosicosidodécaèdre]] |
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Latest revision as of 20:27, 7 May 2024
| Great icosicosidodecahedron | |
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| Type | Uniform star polyhedron |
| Elements | F = 52, E = 120 V = 60 (χ = −8) |
| Faces by sides | 20{3}+12{5}+20{6} |
| Coxeter diagram |    
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| Wythoff symbol | 3/2 5 | 3 3 5/4 | 3 |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U48, C62, W88 |
| Dual polyhedron | Great icosacronic hexecontahedron |
| Vertex figure |  5.6.3/2.6 |
| Bowers acronym | Giid |
In geometry, the great icosicosidodecahedron (or great icosified icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U48. It has 52 faces (20 triangles, 12 pentagons, and 20 hexagons), 120 edges, and 60 vertices.[1] Its vertex figure is a crossed quadrilateral.
Related polyhedra
[edit]It shares its vertex arrangement with the truncated dodecahedron. It additionally shares its edge arrangement with the great ditrigonal dodecicosidodecahedron (having the triangular and pentagonal faces in common) and the great dodecicosahedron (having the hexagonal faces in common).
 Truncated dodecahedron |
Great icosicosidodecahedron |
 Great ditrigonal dodecicosidodecahedron |
 Great dodecicosahedron |
References
[edit]- ^ Maeder, Roman. "48: great icosicosidodecahedron". MathConsult.
External links
[edit]
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