View source for Rhombicosahedron

{{distinguish|Rhombic icosahedron}}
{{Uniform polyhedra db|Uniform polyhedron stat table|rI}}
[[File:Rhombicosahedron.stl|thumb|3D model of a rhombicosahedron]]
In [[geometry]], the '''rhombicosahedron''' is a [[nonconvex uniform polyhedron]], indexed as U<sub>56</sub>. It has 50 faces (30 [[Square|squares]] and 20 [[Hexagon|hexagons]]), 120 edges and 60 vertices.<ref>{{Cite web|url=https://www.mathconsult.ch/static/unipoly/56.html|title=56: rhombicosahedron|last=Maeder|first=Roman|date=|website=MathConsult|archive-url=|archive-date=|access-date=}}</ref> Its [[vertex figure]] is an [[antiparallelogram]].

== Related polyhedra ==

A '''rhombicosahedron''' shares its [[vertex arrangement]] with the [[Polyhedron compound#Uniform compounds|uniform compounds]] of [[compound of ten triangular prisms|10]] or [[compound of twenty triangular prisms|20 triangular prisms]]. It additionally shares its edges with the [[rhombidodecadodecahedron]] (having the square faces in common) and the [[icosidodecadodecahedron]] (having the hexagonal faces in common).

{| class="wikitable" width="400" style="vertical-align:top;text-align:center"
| [[File:Rhombidodecadodecahedron convex hull.png|100px]]<BR>[[Convex hull]]
| [[Image:Rhombidodecadodecahedron.png|100px]]<BR>[[Rhombidodecadodecahedron]]
| [[Image:Icosidodecadodecahedron.png|100px]]<BR>[[Icosidodecadodecahedron]]
|-
| [[Image:Rhombicosahedron.png|100px]]<BR>'''Rhombicosahedron'''
| [[Image:UC32-10 triangular prisms.png|100px]]<BR>[[Compound of ten triangular prisms]]
| [[Image:UC33-20 triangular prisms.png|100px]]<BR>[[Compound of twenty triangular prisms]]
|}
{{Clear}}


==Rhombicosacron==
{{Uniform polyhedra db|Uniform dual polyhedron stat table|rI}}
[[File:Rhombicosacron.stl|thumb|3D model of a rhombicosacron]]
The [[rhombicosacron]] is a nonconvex [[Isohedral figure|isohedral]] [[polyhedron]]. It is the [[Dual polyhedron|dual]] of the [[nonconvex uniform polyhedron|uniform]] rhombicosahedron, U<sub>56</sub>. It has 50 [[Vertex (geometry)|vertices]], 120 [[Edge (geometry)|edges]], and 60 [[crossed-quadrilateral]] faces.

==References==
{{Reflist}}
*{{Citation | last1=Wenninger | first1=Magnus | author1-link=Magnus Wenninger | title=Dual Models | publisher=[[Cambridge University Press]] | isbn=978-0-521-54325-5 |mr=730208 | year=1983}}

== External links ==
* {{mathworld | urlname = Rhombicosacron | title = Rhombicosacron}}
* {{mathworld | urlname = Rhombicosahedron | title = Rhombicosahedron}}
* [http://gratrix.net/polyhedra/uniform/summary Uniform polyhedra and duals]

{{Nonconvex polyhedron navigator}}

[[Category:Uniform polyhedra]]


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