Snub Cube

This function calculates various properties of a snub cube. A snub cube is a solid with 38 faces: 6 squares and 32 equilateral triangles. It has 60 edges and 24 vertices.

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

Snub Cube Calculator  Input Delete Entry Edge length Volume Surface Outer radius Midsphere radius Decimal places 0 1 2 3 4 6  Results Edge length a VolumeV Surface areaS Outer radius rc Midsphere radius rm

Formulas for the Snub Cube

\(\displaystyle t=\frac{1+\sqrt[3]{19+3·\sqrt{33}} +\sqrt[3]{19-3·\sqrt{33}}}{3}≈1.8392867552\)

Volume

\(\displaystyle V=\frac{a^3 · (3 ·\sqrt{t-1} +4· \sqrt{t+1}}{3·\sqrt{2-t}}\)

\(\displaystyle a= \sqrt[3]{ \frac{2 · V ·\sqrt{2-t}}{3·\sqrt{t-1}+4 ·\sqrt{t+1}}} \)

Surface area

\(\displaystyle S= 2 · a^2 ·(3+4·\sqrt{3})\)

\(\displaystyle a= \sqrt{ \frac{S}{2 ·(3+4·\sqrt{3})}} \)

Outer radius

\(\displaystyle rc= a·\sqrt{\frac{3-t}{4·(2-t)}}\)

\(\displaystyle a=\frac{rc}{\sqrt{\displaystyle\frac{3-t}{4·(2-t)}}}\)

Midsphere radius

\(\displaystyle rm= a·\sqrt{\frac{1}{4·(2-t)}}\)

\(\displaystyle a=\frac{rm}{\sqrt{\displaystyle\frac{1}{4·(2-t)}}}\)