Rhombic Triacontahedron (Triacontahedron)
Calculators and formulas for rhombic triacontahedron (also triacontahedron)
This function calculates various parameters of a rhombic triacontahedron (also triacontahedron). Entering one value is sufficient for the calculation; all others are calculated from it.
A rhombic triacontahedron is a Catalan solid. It has 30 rhombic faces, 32 corners and 60 edges. 12 of the corners are bordered by 5 edges and the remaining 20 corners are bordered by 3 edges.
To calculate a rhombic dodecahedron, select the property you know from the menu and enter its value. Then click on the 'Calculate' button.
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Rhombic Triacontahedron Formulas
Surface (\(\small{S}\))
\(\displaystyle S=12·a^2·\sqrt{5}\) \(\displaystyle ≈a^2·26.83\)
Volume (\(\small{V}\))
\(\displaystyle V=4· a^3·\sqrt{5+2·\sqrt{5}}\) \(\displaystyle ≈a^3·12.31\)
Midsphere radius (\(\small{R_K}\))
\(\displaystyle R_K=\frac{a·(5+2·\sqrt{2})}{5}\) \(\displaystyle ≈a·1.45\)
Insphere radius (\(\small{R_I}\))
\(\displaystyle R_I=a·\sqrt{\frac{5+2·\sqrt{5}}{5}}\) \(\displaystyle ≈a·1.38\)
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