skew polygon

More generally regular skew polygons can be defined in n-space.

Their vertex figures are skew polygons, zig-zagging between two planes.

Skew polygons must have at least 4 vertices.

A skew polygon does not lie in a flat plane, but zigzags in three (or more) dimensions.

See skew polygon for more.

In the infinite limit regular skew polygons become skew apeirogons.

In geometry, a skew polygon is a polygon whose vertices do not lie in a plane.

He first realized the importance of the regular skew polygons which appear on the surface of regular polyhedra and higher polytopes.

A regular skew polygon in 3-space can be seen as nonplanar paths zig-zagging between two parallel planes, defined as the side-edges of a uniform antiprism.

But a skew polygon in traditional geometry is 3-dimensional, since it is not flat (planar); while its abstract equivalent, and indeed all abstract polygons, have rank 2.

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

According to Coxeter, in 1926 John Flinders Petrie generalized the concept of regular skew polygons (nonplanar polygons) to regular skew polyhedra.

In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon such that every (n-1) consecutive sides (but no n) belong to one of the facets.

The next five dealt with surfaces applicable to a plane, the area of skew polygons, surface integrals of minimum area with a given bound, and the final note gave the definition of Lebesgue integration for some function f(x).