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In geometry, a skew apeirohedron is an infinite skew polyhedron consisting of nonplanar faces or nonplanar vertex figures, allowing the figure to extend indefinitely without folding round to form a closed surface. Skew apeirohedra have also been called polyhedral sponges. Many are directly related to a convex uniform honeycomb, being the polygonal surface of a honeycomb with some of the cells removed. Characteristically, an infinite skew polyhedron divides 3-dimensional space into two halves. If one half is thought of as ''solid'' the figure is sometimes called a partial honeycomb. == Regular skew apeirohedra == (詳細はCoxeter, in 1926 John Flinders Petrie generalized the concept of regular skew polygons (nonplanar polygons) to ''regular skew polyhedra'' (apeirohedra).〔Coxeter, H. S. M. ''Regular Skew Polyhedra in Three and Four Dimensions.'' Proc. London Math. Soc. 43, 33-62, 1937.〕 Coxeter and Petrie found three of these that filled 3-space: muoctahedron |align=center|150px mutetrahedron |} There also exist chiral skew apeirohedra of types , , and . These skew apeirohedra are vertex-transitive, edge-transitive, and face-transitive, but not mirror symmetric . Beyond Euclidean 3-space, in 1967 C. W. L. Garner published a set of 31 regular skew polyhedra in hyperbolic 3-space.〔Garner, C. W. L. ''Regular Skew Polyhedra in Hyperbolic Three-Space.'' Canad. J. Math. 19, 1179-1186, 1967. ()〕 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「Skew apeirohedron」の詳細全文を読む スポンサード リンク
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