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
Cupola (geometry) Cupola (geometry) In geometry, a cupola is a solid formed by joining two polygons, one (the base) with twice as many edges as the other, by an alternating band of isosceles triangles and rectangles. If the triangles are equilateral and the rectangles are squares, while the base and its opposite face are regular polygons, the triangular, square, and pentagonal cupolae all count among the Johnson solids, and can be formed by taking sections of the cuboctahedron, rhombicuboctahedron, and rhombicosidodecahedron, respectively. A cupola can be seen as a prism where one of the polygons has been collapsed in half by merging