Skew polygon Skew polygon In geometry, a skew polygon is a polygon whose vertices are not all coplanar. Skew polygons must have at least 4 vertices. The "interior" surface (or area) of such a polygon is not uniquely defined. Skew infinite polygons (apeirogons) have vertices which are not all collinear. A zig-zag skew polygon or antiprismatic polygon has vertices which alternate on two parallel planes, and thus must be even-sided. Regular skew polygon in 3 dimensions (and regular skew apeirogons in 2 dimensions) are always zig-zag. A regular skew polygon is isogonal with equal edge lengths. In 3 dimensions a regular skew
Regular 4-polytope are 4 dual-pairs and 2 self-dual forms among the ten regular star polychora. Note: The cells (polyhedra), their faces (polygons), the "polygonal edge figures" and "polyhedral vertex figures" are identified by their Schläfli symbols. Regular 4-polytope In mathematics, a regular 4-polytope is a regular four-dimensional polytope. They are the four-dimensional analogs of the regular polyhedra in three dimensions and the regular polygons in two dimensions. Regular 4-polytopes were first described by the Swiss mathematician Ludwig Schläfli in the mid-19th century, although the full set were not discovered until later. There are six convex and ten star regular 4-polytopes, giving a