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(unless ''p''/''q''=2), 4''np'' triangles |- |bgcolor=#e7dcc3|Edges||8''np'' |- |bgcolor=#e7dcc3|Vertices||4''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: 2''p''-fold improper rotation (S2''p'') *''q'' even: ''p''-fold rotation (C''p''h) |} Each member of this infinite family of uniform polyhedron compounds is a symmetric arrangement of antiprisms sharing a common axis of rotational symmetry. It arises from superimposing two copies of the corresponding prismatic compound of antiprisms (without rotational freedom), and rotating each copy by an equal and opposite angle. This infinite family can be enumerated as follows: *For each positive integer ''n''>0 and for each rational number ''p''/''q''>3/2 (expressed with ''p'' and ''q'' coprime), there occurs the compound of 2''n'' ''p''/''q''-gonal antiprisms (with rotational freedom), with symmetry group: * *D''np''d if ''nq'' is odd * *D''np''h if ''nq'' is even Where ''p''/''q''=2 the component is a tetrahedron, sometimes not considered a true antiprism. == References == *. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Prismatic compound of antiprisms with rotational freedom」の詳細全文を読む スポンサード リンク
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