Regular Skew Polygons
The cube contains a skew regular hexagon, seen as 6 red edges zig-zagging between two planes perpendicular to the cube's diagonal axis. |
The zig-zagging side edges of a n-antiprism represent a regular skew 2n-gon, as show in this 17-gonal antiprism. |
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. All edges and internal angles are equal.
The Platonic solids (the tetrahedron, cube, octahedron, dodecahedron, and icosahedron) have Petrie polygons, seen in red here, with sides 4, 6, 6, 10, and 10 respectively. |
More generally regular skew polygons can be defined in n-space. Examples include the Petrie polygons, polygonal paths of edges that divide a regular polytope into two halves, and seen as a regular polygon in orthogonal projection.
In the infinite limit regular skew polygons become skew apeirogons.
Read more about this topic: Regular Polygon
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—Henry David Thoreau (1817–1862)