Two-dimensional Regular Polytopes
The two dimensional polytopes are called polygons. Regular polygons are equilateral and cyclic. A p-gonal regular polygon is represented by Schläfli symbol {p}.
Usually only convex polygons are considered regular, but star polygons, like the pentagram, can also be considered regular. They use the same vertices as the convex forms, but connect in an alternate connectivity which passes around the circle more than once to complete.
Star polygons should be called nonconvex rather than concave because the intersecting edges do not generate new vertices and all the vertices exist on a circle boundary.
Read more about this topic: List Of Regular Polytopes
Famous quotes containing the word regular:
“A regular council was held with the Indians, who had come in on their ponies, and speeches were made on both sides through an interpreter, quite in the described mode,—the Indians, as usual, having the advantage in point of truth and earnestness, and therefore of eloquence. The most prominent chief was named Little Crow. They were quite dissatisfied with the white man’s treatment of them, and probably have reason to be so.”
—Henry David Thoreau (1817–1862)