Irregular Star Polygons
A star polygon need not be regular. Irregular cyclic star polygons occur as vertex figures for the uniform polyhedra, defined by the sequence of regular polygon faces around each vertex, allowing for both multiple turns, and retrograde directions. (See vertex figures at List of uniform polyhedra)
The unicursal hexagram is another example of a cyclic irregular star polygon, containing only D2h Dihedral symmetry.
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