Rhombicuboctahedron
Calculator and formulas for calculating a rhombicuboctahedron
This function calculates various properties of a rhombicuboctahedron. A rhombicuboctahedron is made up of 8 equilateral triangles and 18 squares. Viewed perpendicular to a square, it has the shape of a regular octagon.
To perform the calculation, select the property you know and enter its value. Then click on the 'Calculate' button.
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Rhombicuboctahedron formula
Volume \(\small{V}\)
\(\displaystyle V= \frac{2· a^3 · (6+5·\sqrt{2})}{3}\)
Surface \(\small{S}\)
\(\displaystyle S= 2 · a^2 ·(9+\sqrt{3})\)
Outer radius \(\small{r_c}\)
\(\displaystyle r_c=\frac{a·\sqrt{5+2·\sqrt{2}}}{2} \)
Midsphere radius \(\small{r_m}\)
\(\displaystyle r_m=\frac{a·\sqrt{4+2·\sqrt{2}}}{2}\)
Edge length \(\small{a}\)
\(\displaystyle a= \sqrt[3]{ \frac{3· V }{2 ·(6+5· \sqrt{2})}} \)
\(\displaystyle a= \sqrt{ \frac{S}{2·(9+\sqrt{3})}} \)
\(\displaystyle a=\frac{2·r_c}{ \sqrt{5+2·\sqrt{2}}} \)
\(\displaystyle a= \frac{2 ·r_m}{\sqrt{4+2·\sqrt{2}}} \)