Icositetragon
In geometry, an icositetragon (or icosikaitetragon or tetracosagon) is a twenty-four-sided polygon or 24-gon. The sum of any icositetragon's interior angles is 3960 degrees.
Regular 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}.
One interior angle in a regular icositetragon is 165°, meaning that one exterior angle would be 15°.
The area of a regular icositetragon is: (with t = edge length)
The icositetragon appeared in Archimedes' polygon approximation of pi, along with the hexagon (6-gon), dodecagon (12-gon), tetracontaoctagon (48-gon), and enneacontahexagon (96-gon).
Construction
As 24 = 23 × 3, a regular icositetragon is constructible using a compass and straightedge. As a truncated dodecagon, it can be constructed by an edge-bisection of a regular dodecagon.
Symmetry
The regular icositetragon has Dih24 symmetry, order 48. There are 7 subgroup dihedral symmetries: (Dih12, Dih6, Dih3), and (Dih8, Dih4, Dih2 Dih1), and 8 cyclic group symmetries: (Z24, Z12, Z6, Z3), and (Z8, Z4, Z2, Z1).
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