Great Stellated Dodecahedron Calculation

This function calculates the height or volume of a great stellated dodecahedron.

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

Stellated Dodecahedron Calculator  Input Delete Entry Side length a Edge length s Volume Surface area Circle radius Height Decimal places 0 1 2 3 4 6   Results Side length a Edge length s Chord length c Volume V Surface area S Circle radius r Height h

Formulas of a Great Stellated Dodecahedron

Edge length	\(\displaystyle s = \frac{a}{2} \cdot (1 + \sqrt{5})\) \(\displaystyle \;\;\; ≈ a \cdot 1,618\)
Chord length	\(\displaystyle c = a \cdot (2 + \sqrt{5})\) \(\displaystyle \;\;\; ≈ a \cdot 4.236\)
Volume	\(\displaystyle V=\frac{5}{4} \cdot a^3 \cdot (3 + \sqrt{5})\) \(\displaystyle \;\;\; ≈ a^3 \cdot 6.545\)
Surface area	\(\displaystyle S= 15\cdot a^2 \cdot \sqrt{5 + 2 \cdot \sqrt{5}}\) \(\displaystyle \;\;\; ≈ a^2 \cdot 46.165\)
Circumsphere radius	\(\displaystyle r=\frac{a}{4} \cdot \sqrt{3} \cdot (3 + \sqrt{5})\) \(\displaystyle \;\;\; ≈ a \cdot 2.267\)
Height	\(\displaystyle h = \frac{a}{6} \cdot \sqrt{3} \cdot (3 + \sqrt{5})\) \(\displaystyle \;\;\; ≈ a \cdot 1.512 \)