Schläfli symbol, opinions differ as to the nature of the degenerate figure. For example, {6/2} may be treated in either of two ways: For much of the 20th century (see for example ), we have commonly taken the /2 to indicate joining each vertex of a convex {6} to its near neighbors two steps away, to obtain the regular compound of two triangles, or hexagram. Coxeter clarifies this regular compound with a notation {kp}[k{p}]{kp} for the compound {p/k}, so the hexagram is represented as {6}[2{3}]{6}. More compactly Coxeter also writes 2{n/2}, like 2{3} for a hexagram as compound as alternations of regular even-sided polygons, with italics on the leading factor to differentiate it from the coinciding interpretation. Many modern geometers, such as Grünbaum (2003), regard this as incorrect. They take the /2 to indicate moving two places around the {6} at each step, obtaining a "double-wound" triangle that has two vertices superimposed at each corner point and two edges along each line segment. Not only does this fit in better with modern theories of abstract polytopes, but it also more closely copies the way in which Poinsot (1809) created his star polygons – by taking a single length of wire and bending it at successive points through the same angle until the figure closed. Duality of regular polygons All regular polygons are self-dual to congruency, and for odd n they are self-dual to identity. In addition, the regular star figures (compounds), being composed of regular polygons, are also self-dual. Regular polygons as faces of polyhedra A uniform polyhedron has regular polygons as faces, such that for every two vertices there is an isometry mapping one into the other (just as there is for a regular polygon). A quasiregular polyhedron is a uniform polyhedron which has just two kinds of face alternating around each vertex. A regular polyhedron is a uniform polyhedron which has just one kind of face. The remaining (non-uniform) convex polyhedra with regular faces are known as the Johnson solids. A polyhedron having regular triangles as faces is called a deltahedron. See also Euclidean tilings by convex regular polygons Platonic solid Apeirogon – An infinite-sided polygon can also be regular, {∞}. List of regular polytopes and compounds Equilateral polygon Carlyle circle Notes References Lee, Hwa Young; "Origami-Constructible Numbers". Grünbaum, B.; Are your polyhedra the same as my polyhedra?, Discrete and comput. geom: the Goodman-Pollack festschrift, Ed. Aronov et