Regular polygon common angle is a constructible number—that is, can be written in terms of the four basic arithmetic operations and the extraction of square roots. 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. 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
Euclidean tilings by convex regular polygons figures, which are also called "m"-Archimedean tilings. For edge-to-edge Euclidean tilings, the internal angles of the polygons meeting at a vertex must add to 360 degrees. A regular -gon has internal angle formula_1 degrees. There are seventeen combinations of regular polygons whose internal angles add up to 360 degrees, each being referred to as a "species" of vertex; in four cases there are two distinct cyclic orders of the polygons, yielding twenty-one "types" of vertex. Only eleven of these can occur in a uniform tiling of regular polygons, given in previous sections. In particular, if three polygons meet at a