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prismatic compound of antiprisms : ウィキペディア英語版
prismatic compound of antiprisms

ßr
|-
|bgcolor=#e7dcc3|Coxeter diagrams
(n=2)||
|-
|bgcolor=#e7dcc3|Faces||2''n'' (unless ''p''/''q''=2), 2''np'' triangles
|-
|bgcolor=#e7dcc3|Edges||4''np''
|-
|bgcolor=#e7dcc3|Vertices||2''np''
|-
|bgcolor=#e7dcc3|Symmetry group||
*''nq'' odd: ''np''-fold antiprismatic (D''np''d)
*''nq'' even: ''np''-fold prismatic (D''np''h)
|-
|bgcolor=#e7dcc3|Subgroup restricting to one constituent||
*''q'' odd: ''p''-fold antiprismatic (D''p''d)
*''q'' even: ''p''-fold prismatic (D''p''h)
|}
In geometry], a prismatic compound of antiprism is a category of uniform polyhedron compound. Each member of this infinite family of uniform polyhedron compounds is a symmetric arrangement of antiprisms sharing a common axis of rotational symmetry.
== Infinite family ==
This infinite family can be enumerated as follows:
*For each positive integer ''n''≥1 and for each rational number ''p''/''q''>3/2 (expressed with ''p'' and ''q'' coprime), there occurs the compound of ''n'' ''p''/''q''-gonal antiprisms, with symmetry group:
*
*D''np''d if ''nq'' is odd
*
*D''np''h if ''nq'' is even
Where ''p''/''q''=2, the component is the tetrahedron (or dyadic antiprism). In this case, if ''n''=2 then the compound is the stella octangula, with higher symmetry (Oh).

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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