How many edges has a pentadecagon?
Pentadecagon order of the symmetry follows the letter. He gives r30 for the full reflective symmetry, Dih. He gives d (diagonal) with reflection lines through vertices, p with reflection lines through edges (perpendicular), and for the odd-sided pentadecagon i with mirror lines through both vertices and edges, and g for cyclic symmetry. a1 labels no symmetry. These lower symmetries allows degrees of freedoms in defining irregular pentadecagons. Only the g15 subgroup has no degrees of freedom but can seen as directed edges. There are three regular star polygons: {15/2}, {15/4}, {15/7}, constructed from the same 15 vertices of a regular pentadecagon,
Pentadecagon but connected by skipping every second, fourth, or seventh vertex respectively. There are also three regular star figures: {15/3}, {15/5}, {15/6}, the first being a compound of three pentagons, the second a compound of five equilateral triangles, and the third a compound of three pentagrams. Deeper truncations of the regular pentadecagon and pentadecagrams can produce isogonal (vertex-transitive) intermediate star polygon forms with equal spaced vertices and two edge lengths. The regular pentadecagon is the Petrie polygon for some higher-dimensional polytopes, projected in a skew orthogonal projection: It is also the Petrie polygon for the great 120-cell and grand stellated 120-cell.