Icosikaitetragon

The amount of space a regular icosikaitetragon takes up is

The area of a regular icosikaitetragon of side length a is given by

${\displaystyle A=6a^{2}\cot {\frac {\pi }{24}}=6a^{2}(2+{\sqrt {2}}+{\sqrt {3}}+{\sqrt {6}})\simeq 45.5745a^{2}.}$