Icosahedron calculator
Online calculator and formulas to calculate an icosahedron
This function calculates various properties of an icosahedron. An icosahedron is a solid with 20 sides, 30 edges and 12 vertices.
To perform the calculation, select the property you know and enter its value. Then click the Calculate button.
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Icosahedron Formulas
Volume (\(\small{V}\))
\(\displaystyle V=\frac{5}{12}· a^3·(3+\sqrt{5})\)
Surface area (\(\small{S}\))
\(\displaystyle S= 5 · a^2 · \sqrt{3}\)
Circum radius (\(\small{R_c}\))
\(\displaystyle R_c=\frac{a}{4} · \sqrt{10 + 2 · \sqrt{5}} \)
Mid radius (\(\small{R_m}\))
\(\displaystyle R_m=\frac{a}{4} · (1 +\sqrt{5}) \)
Inner radius (\(\small{R_i}\))
\(\displaystyle R_i=\frac{a}{12} · \sqrt{3} ·(3 +\sqrt{5}) \)
Diagonal (\(\small{d}\))
\(\displaystyle d=2 · R_c \)
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