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In geometry, an apeirogonal antiprism or infinite antiprism〔Conway (2008), p. 263〕 is the arithmetic limit of the family of antiprisms; it can be considered an infinite polyhedron or a tiling of the plane. If the sides are equilateral triangles, it is a uniform tiling. In general, it can have two sets of alternating congruent isosceles triangles, surrounded by two half-planes. == Related tilings and polyhedra == The apeirogonal antiprism is the arithmetic limit of the family of antiprisms sr or ''p''.3.3.3, as ''p'' tends to infinity, thereby turning the antiprism into a Euclidean tiling. It can be constructed by an alternation operation applied to an apeirogonal prism: : Its dual tiling is an ''apeirogonal deltohedron'': :240px Similarly to the uniform polyhedra and the uniform tilings, eight uniform tilings may be based from the regular apeirogonal tiling. The rectified and cantellated forms are duplicated, and as two times infinity is also infinity, the truncated and omnitruncated forms are also duplicated, therefore reducing the number of unique forms to four: the apeirogonal tiling, the apeirogonal hosohedron, the apeirogonal prism, and the apeirogonal antiprism. !r !t ! !rr !tr !sr |- !Coxeter ! ! ! ! ! ! ! ! |- align=center |Image Vertex figure |60px |60px ∞.∞ |60px ∞.∞ |60px 4.4.∞ |60px |60px 4.4.∞ |60px 4.4.∞ |60px 3.3.3.∞ |} 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「apeirogonal antiprism」の詳細全文を読む スポンサード リンク
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