Compound of twenty triangular prisms: Difference between revisions

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{{Short description|Polyhedral compound}}

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{|class="wikitable" style="float:right; margin-left:8px; width:250px"

!bgcolor=#e7dcc3 colspan=2|Compound of twenty triangular prisms

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|align=center colspan=2|[[Image:UC33-20_triangular_prisms20 triangular prisms.png|200px]]

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|bgcolor=#e7dcc3|Type||[[Uniform polyhedron compound|Uniform compound]]

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|bgcolor=#e7dcc3|Index||UC₃₃

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|bgcolor=#e7dcc3|Polyhedra||20 [[triangular prism|triangular prisms]]s

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|bgcolor=#e7dcc3|Faces||40 [[triangle]]s, 60 [[Square (geometry)|squares]]

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|bgcolor=#e7dcc3|Edges||180

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|bgcolor=#e7dcc3|Vertices||60

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|bgcolor=#e7dcc3|[[Symmetry group]]||[[Icosahedral symmetry|icosahedral]] (''I''_h'')

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|bgcolor=#e7dcc3|[[Subgroup]] restricting to one constituent||3-fold [[Dihedral symmetry in three dimensions|dihedral]] (''D''₃'')

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This [[uniform polyhedron compound]] is a symmetric arrangement of 20 [[triangular prism|triangular prisms]]s, aligned in pairs with the axes of three-fold rotational symmetry of an [[icosahedron]]. It results from composing the two [[enantiomorphs]] of the [[compound of ten triangular prisms|compound of 10 triangular prisms]].

It results from composing the two [[enantiomorphs]] of the [[compound of ten triangular prisms|compound of 10 triangular prisms]]. In doing so, the vertices of the two enantiomorphs coincide, with the result that the full compound has two triangular prisms incident on each of its vertices.

It shares its vertices with the [[rhombidodecadodecahedron]].

== Related polyhedra ==

This compound shares its [[vertex arrangement]] with three [[uniform polyhedron|uniform polyhedra]] as follows:

{| 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]]

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| [[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

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== References ==

* [[{{citation|first=John |last=Skilling]], ''|title=Uniform Compounds of Uniform Polyhedra'', |journal=[[Mathematical Proceedings of the Cambridge Philosophical Society, Vol. ]]|volume=79, pp. 447-457, |issue=3|pages=447–457|year=1976|doi=10.1017/S0305004100052440|mr=0397554}}.

[[Category:Polyhedral compounds]]

{{polyhedron-stub}}