Skew apeirotopes Apeirotope

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a skew apeirogon in 2 dimensions forms zig-zag line in plane. if zig-zag , symmetrical, apeirogon regular.


skew apeirogons can constructed in number of dimensions. in 3 dimensions, regular skew apeirogon traces out helical spiral , may either left- or right-handed.


infinite skew polyhedra

there 3 regular skew apeirohedra, rather polyhedral sponges:



6 squares around each vertex, coxeter symbol {4,6|4}
4 hexagons around each vertex, coxeter symbol {6,4|4}
6 hexagons around each vertex, coxeter symbol {6,6|3}

there thirty regular apeirohedra in euclidean space. these include listed above, (in plane) polytopes of type: {∞,3}, {∞,4}, {∞,6} , in 3-dimensional space, blends of these either apeirogon or line segment, , pure 3-dimensional apeirohedra (12 in number)








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