Skew polygon

In geometry, a skew polygon is a closed polygonal chain in Euclidean space. It is a figure similar to a polygon except its vertices are not all coplanar.^[1] While a polygon is ordinarily defined as a plane figure, the edges and vertices of a skew polygon form a space curve. Skew polygons must have at least four vertices. The interior surface and corresponding area measure of such a polygon is not uniquely defined.

Skew infinite polygons (apeirogons) have vertices which are not all colinear.

A zig-zag skew polygon or antiprismatic polygon^[2] has vertices which alternate on two parallel planes, and thus must be even-sided.

Regular skew polygons in 3 dimensions (and regular skew apeirogons in two dimensions) are always zig-zag.

^ Coxeter 1973, §1.1 Regular polygons; "If the vertices are all coplanar, we speak of a plane polygon, otherwise a skew polygon."
^ Regular complex polytopes, p. 6

[FOOTNOTECoxeter1973§1.1_Regular_polygons-1] Coxeter 1973, §1.1 Regular polygons; "If the vertices are all coplanar, we speak of a plane polygon, otherwise a skew polygon."

[rcp-2] Regular complex polytopes, p. 6

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