Pentakis Dodecahedron
Calculators and formulas for the pentakis dodecahedron
This function calculates various parameters of a pentakis dodecahedron. Entering one value is sufficient for the calculation; all others are calculated from it.
The pentakis dodecahedron is a convex polyhedron composed of 60 isosceles triangles. It has 32 corners and 90 edges. For more information, see Wikipedia.
To perform the calculation select the property you know from the menu and enter its value. Then click on the 'Calculate' button.
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Pentakis Dodecahedron Formulas
Base length (\(\small{a}\))
\(\displaystyle a= \frac{38 ·b}{3·(9+\sqrt{5})}\) \(\displaystyle \ \ \ ≈1.27 ·b\)
Leg length (\(\small{b}\))
\(\displaystyle b= \frac{3·a·(9+\sqrt{5})}{38}\) \(\displaystyle ≈0.887 ·a\)
Surface (\(\small{S}\))
\(\displaystyle S=\frac{15·a^2·\sqrt{413+162·\sqrt{5}}}{19}\) \(\displaystyle ≈ a^2 ·21.98\)
Volume (\(\small{V}\))
\(\displaystyle V=\frac{15·a^3·(23+11·\sqrt{5})}{76}\) \(\displaystyle ≈9.394 ·a^3\)
Midsphere radius (\(\small{R_K}\))
\(\displaystyle R_K=\frac{a ·(3+\sqrt{5})}{4}\) \(\displaystyle a·1.31\)
Insphere radius (\(\small{R_I}\))
\(\displaystyle R_I=\frac{3· a}{2}·\sqrt{\displaystyle\frac{81+35·\sqrt{5}}{218}}\) \(\displaystyle ≈a ·1.28\)
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