Triakis Icosahedron
Calculators and formulas for triakis icosahedron
This function calculates various parameters of a triakis octahedron. Entering one value is sufficient for the calculation; all others are calculated from it.
The triakisicosahedron is a convex polyhedron composed of 60 isosceles triangles. It is dual to the truncated dodecahedron and has 32 vertices and 90 edges. For more information, see Wikipedia.
To calculate, select the property you know from the menu and enter its value. Then click on the 'Calculate' button.
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Triakis Icosahedron Formulas
Long edge (\(\small{a}\))
\(\displaystyle a=\frac{22·b}{15-\sqrt{5})}\) \(\displaystyle \ \ \ ≈1.724·b\)
Short edge (\(\small{b}\))
\(\displaystyle b=\frac{a·(15-\sqrt{5})}{22}\) \(\displaystyle \ \ \ ≈a·0.58\)
Surface (\(\small{S}\))
\(\displaystyle S=\frac{15·a^2·\sqrt{109-30·\sqrt{5}}}{11}\) \(\displaystyle \ \ \ ≈a^2·8.829\)
Volume (\(\small{V}\))
\(\displaystyle V=\frac{5 ·a^3·(5+7·\sqrt{5})}{44}\) \(\displaystyle \ \ \ ≈a^3·2.347\)
Midsphere radius (\(\small{R_K}\))
\(\displaystyle R_K=\frac{a·(1+\sqrt{5})}{4}\) \(\displaystyle \ \ \ ≈a·0.809\)
Insphere radius (\(\small{R_I}\))
\(\displaystyle R_I=\frac{a}{4} ·\sqrt{\frac{10·(33+13·\sqrt{5})}{61}}\) \(\displaystyle \ \ \ ≈a·0.797\)
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