The regular dodecagon, illustrated above, is the constructible 12-sided regular polygon that can be denoted using the Schläfli symbol {12}. The Australian 50-cent piece is dodecagonal, as illustrated above. The inradius r, circumradius R, and area A can be computed directly from the formulas for a general regular polygon with side length a and n=12 sides, r = 1/2acot(pi/(12)) (1) = 1/2(2+sqrt(3))a (2) R = 1/2acsc(pi/(12)) (3) = 1/2(sqrt(2)+sqrt(6))a (4) A = 1/4na^2cot(pi/(12)) (5)...