Icositetragon

The regular icositetragon is represented by Schläfli symbol {24} and can also be constructed as a truncated dodecagon, t{12}, or a twice-truncated hexagon, tt{6}, or thrice-truncated triangle, ttt{3}.

Coxeter states that every zonogon (a 2m-gon whose opposite sides are parallel and of equal length) can be dissected into m(m-1)/2 parallelograms.

[3] In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi.

A regular triangle, octagon, and icositetragon can completely fill a plane vertex.

In 3-dimensions it will be a zig-zag skew icositetragon and can be seen in the vertices and side edges of a dodecagonal antiprism with the same D12d, [2+,24] symmetry, order 48.

The regular icositetragon is the Petrie polygon for many higher-dimensional polytopes, seen as orthogonal projections in Coxeter planes, including:

Symmetries of a regular icositetragon. Vertices are colored by their symmetry positions. Blue mirrors are drawn through vertices, and purple mirrors are drawn through edge. Gyration orders are given in the center.