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|[[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]]. 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.

== Related polyhedra ==

ItThis compound shares its [[vertex arrangement]] with thethree [[rhombidodecadodecahedronuniform 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]]

| [[Image:Rhombicosahedron.png|100px]]<BR>[[Rhombicosahedron]]

|-

| [[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]]

|}

== References ==

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

[[Category:Polyhedral compounds]]

{{polyhedron-stub}}

[[eo:Kombinaĵo de 20 triangulaj prismoj]]

{{polyhedron-stub}}