Hexakis Octahedron
Calculators and formulas for the hexakis octahedron (also disdyakis dodecahedron)
This function calculates various parameters of a hexakis octahedron (also disdyakis dodecahedron). Entering one value is sufficient for the calculation; all others are calculated from it.
The hexakis octahedron is a convex polyhedron composed of 48 irregular triangles. It is dual to the truncated cuboctahedron and has 26 vertices and 72 edges.
To perform the calculation select the property you know from the menu and enter its value. Then click on the 'Calculate' button.
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Hexakis Octahedron Formulas
Long edge (\(\small{a}\))
\(\displaystyle a=\frac{14·b}{3·(1+2·\sqrt{2})}\) \(\displaystyle \ \ \ ≈1.22·b\)
Medium edge (\(\small{b}\))
\(\displaystyle b=\frac{3· a·(1+2·\sqrt{2})}{14}\) \(\displaystyle \ \ \ ≈\frac{a}{1.22}\)
Short edge (\(\small{c}\))
\(\displaystyle c=\frac{a·(10-\sqrt{2})}{14}\) \(\displaystyle \ \ \ ≈\frac{a}{1.63}\)
Surface e (\(\small{S}\))
\(\displaystyle S=\frac{3·a^2·\sqrt{543+176·\sqrt{2}}}{7}\) \(\displaystyle \ \ \ ≈a^2·12.06\)
Volume (\(\small{V}\))
\(\displaystyle V=\frac{a^3·\sqrt{6·(986+607·\sqrt{2})}}{28}\) \(\displaystyle \ \ \ ≈a^3·3.757\)
Midsphere radius (\(\small{R_K}\))
\(\displaystyle R_K=\frac{a·(1+2·\sqrt{2})}{4}\) \(\displaystyle \ \ \ ≈a·0.957\)
Insphere radius (\(\small{R_I}\))
\(\displaystyle R_I=\frac{a·\sqrt{\frac{402+195·\sqrt{2}}{194}}}{2}\) \(\displaystyle \ \ \ ≈a·0.935\)
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