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
Skew polygon petrie polygon has. This is 5 sides for a 5-cell, 8 sides for a tesseract and 16-cell, 12 sides for a 24-cell, and 30 sides for a 120-cell and 600-cell. When orthogonally projected onto the Coxeter plane these regular skew polygons appear as regular polygon envelopes in the plane. The "n"-"n" duoprism and dual duopyramids also have 2"n"-gonal petrie polygons. (The tesseract is a 4-4 duoprism, and the 16-cell is a 4-4 duopyramid.) 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