109.241.162.167: distance of text from the table

2025-04-21T18:59:47Z

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{{Short description|Polyhedral compound}}
{| class=wikitable style="float:right; margin-left:8px; width:250px"
!bgcolor=#e7dcc3 colspan=2|Compound of six decagonal prisms
|-
|align=center colspan=2|[[Image:UC40-6 decagonal prisms.png|200px]]
|-
|bgcolor=#e7dcc3|Type||[[Uniform polyhedron compound|Uniform compound]]
|-
|bgcolor=#e7dcc3|Index||UC40
|-
|bgcolor=#e7dcc3|Polyhedra||6 [[decagonal prism]]s
|-
|bgcolor=#e7dcc3|Faces||12 [[decagon]]s, 60 [[Square (geometry)|squares]]
|-
|bgcolor=#e7dcc3|Edges||180
|-
|bgcolor=#e7dcc3|Vertices||120
|-
|bgcolor=#e7dcc3|[[Symmetry group]]||[[Icosahedral symmetry|icosahedral]] (''I''h)
|-
|bgcolor=#e7dcc3|[[Subgroup]] restricting to one constituent||5-fold [[Dihedral symmetry in three dimensions|antiprismatic]] (''D''5d)
|}
This [[uniform polyhedron compound]] is a symmetric arrangement of 6 [[decagonal prism]]s, aligned with the axes of fivefold rotational symmetry of a [[dodecahedron]].

== Cartesian coordinates ==
[[Cartesian coordinates]] for the vertices of this compound are all the cyclic permutations of

: (±√(τ−1/√5), ±2τ, ±√(τ/√5))
: (±(√(τ−1/√5)−τ2), ±1, ±(√(τ/√5)+τ))
: (±(√(τ−1/√5)−τ), ±τ2, ±(√(τ/√5)+1))
: (±(√(τ−1/√5)+τ), ±τ2, ±(√(τ/√5)−1))
: (±(√(τ−1/√5)+τ2), ±1, ±(√(τ/√5)−τ))

where τ = (1+√5)/2 is the [[golden ratio]] (sometimes written φ).

== 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|bibcode=1976MPCPS..79..447S |mr=0397554|s2cid=123279687 }}.

[[Category:Polyhedral compounds]]

{{polyhedron-stub}}

Compound of six decagonal prisms - Revision history

109.241.162.167: distance of text from the table