Truncated Cuboctahedron

This function calculates various properties of a truncated cuboctahedron. A truncated cuboctahedron has 12 square faces, 8 regular hexagonal faces, 6 regular octagonal faces, 48 vertices, and 72 edges.

To perform the calculation, select the property you know and enter its value. Then click on the 'Calculate' button.

Truncated Cuboctahedron calculator  Input Delete Entry Edge length Volume Surface area Outerradius Midsphere radius Decimal places 0 1 2 3 4 6  Results Edge length a Volume V Surface area S Outer radius rc Midsphere radiusrm

Formulas for the truncated cuboctahedron

Volume

\(\displaystyle V= 2· a^3 · (11+7·\sqrt{2})\)

\(\displaystyle a= \sqrt[3]{ \frac{V}{2 ·(11+7· \sqrt{2})}} \)

Surface area

\(\displaystyle S= 12 · a^2 ·(2+\sqrt{2}+\sqrt{3})\)

\(\displaystyle a= \sqrt{ \frac{S}{12·(2+\sqrt{2}+\sqrt{3})}} \)

Outer radius

\(\displaystyle rc=\frac{a·\sqrt{13+6·\sqrt{2}}}{2} \)

\(\displaystyle a=\frac{2·rc}{ \sqrt{13+6·\sqrt{2}}} \)

Midsphere radius

\(\displaystyle rm=\frac{a·\sqrt{12+6·\sqrt{2}}}{2}\)

\(\displaystyle a= \frac{2 ·rm}{\sqrt{12+6·\sqrt{2}}} \)