Snub Dodecahedron
Calculator and formulas for calculating a snub dodecahedron
This function calculates various properties of a snub Dodecahedron The snub dodecahedron has 92 faces, 12 are pentagons and the other 80 are equilateral triangles. It also has 150 edges, and 60 vertices.
To perform the calculation, select the property you know and enter its value. Then click on the 'Calculate' button.
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Snub Dodecahedron Formulas
Golden ratio
\(\displaystyle φ = \frac{1+\sqrt{5}}{2}≈1.6180339887\)
Cosine of the smaller central angle ΞΆ in the chord pentagon
\(\displaystyle t= \frac{1}{12} (\sqrt[3]{44+12· φ·(9+\sqrt{81·φ-15})} \) \(\displaystyle +\sqrt[3]{44+12·φ ·(9-\sqrt{81·φ-15})}-4)\)
\(\displaystyle t ≈ 0.47157562962194088 \)
Volume \(\small{V}\)
\(\displaystyle V=\frac{a^3}{6·\sqrt{1-2t}}\) \(\displaystyle · \left(3·\sqrt{10·(9t-2+(4t-1)\sqrt{5})}+20\sqrt{2+2t}\right) \)
Surface area \(\small{S}\)
\(\displaystyle S= a^2 ·\left(20 ·\sqrt{3}+3·\sqrt{25+10·\sqrt{5}}\right)\)
Outer radius \(\small{r_c}\)
\(\displaystyle r_c=\frac{a}{2}·\sqrt{\frac{2-2t}{1-2t}}\)
Midsphere radius \(\small{r_m}\)
\(\displaystyle r_m= \frac{a}{2· \sqrt{1-2t}}\)
Edge length \(\small{a}\)
\(\displaystyle a= \sqrt[3]{ \frac{6·\sqrt{1-2t}·V}{3·\sqrt{10·(9t-2+(4t-1)\sqrt{5})}+20\sqrt{2+2t}}}\)
\(\displaystyle a= \sqrt{ \frac{S}{20 ·\sqrt{3}+3·\sqrt{25+10·\sqrt{5}}}} \)
\(\displaystyle a=\frac{2· r_c}{\sqrt{\displaystyle\frac{2-2t}{1-2t}}}\)
\(\displaystyle a= r_m · 2· \sqrt{1-2t}\)
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