Skew polygon

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An example of a regular skew quadrilateral, with equal edge lengths, and vertex-transitive, fitted within a rectangular cuboid. Its interior can be uniquely defined as a bilinear interpolation of the four corners and edges. Here the four equal edges are shown in blue, and equal diagonals in green.

In geometry, a skew polygon, saddle polygon, or space polygon, is a polygon whose vertices do not lie in a plane. Skew polygons must have at least 4 vertices.

A regular skew polygon is a skew polygon with equal edge lengths and which is vertex-transitive.

The interior surface (or area) of such a polygon is not uniquely defined, although this can be considered as a minimal surface problem like the form of a soap film inside of a wire frame.

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References[edit]

  • Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X.  "Skew Polygons (Saddle Polygons)." §2.2
  • John Milnor: On the total curvature of knots, Ann. Math. 52 (1950) 248–257.
  • J.M. Sullivan: Curves of finite total curvature, ArXiv:math.0606007v2

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