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.

Rhombicuboctahedron calculator  Eingabe Delete Entry Edge length Volume Surface area Outer radius Midsphere radius Decimal places 0 1 2 3 4 6  Resultate Edge length a Volume V Surface S Outer radius rc Midsphere radius rm

Formulas for the rhombicuboctahedron

Volume

\(\displaystyle V= \frac{2· a^3 · (6+5·\sqrt{2})}{3}\)

\(\displaystyle a= \sqrt[3]{ \frac{3· V }{2 ·(6+5· \sqrt{2})}} \)

Surface area

\(\displaystyle S= 2 · a^2 ·(9+\sqrt{3})\)

\(\displaystyle a= \sqrt{ \frac{S}{2·(9+\sqrt{3})}} \)

Outer radius

\(\displaystyle rc=\frac{a·\sqrt{5+2·\sqrt{2}}}{2} \)

\(\displaystyle a=\frac{2·rc}{ \sqrt{5+2·\sqrt{2}}} \)

Midsphere radius

\(\displaystyle rm=\frac{a·\sqrt{4+2·\sqrt{2}}}{2}\)

\(\displaystyle a= \frac{2 ·rm}{\sqrt{4+2·\sqrt{2}}} \)