Disdyakis Triacontahedron
Calculators and formulas for the disdyakis triacontahedron
This function calculates various parameters of a disdyakis triacontahedron. Entering one value is sufficient for the calculation; all others are calculated from it.
The hexakisicosahedron or disdyakistriacontahedron is a convex polyhedron composed of 120 irregular triangles. It has 62 vertices and 180 edges.
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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Disdyakis Triacontahedron Formulas
Surface (\(\small{S}\))
\(\displaystyle S=\frac{15}{44}· a^2·\sqrt{10·(417+107·\sqrt{5})}\) \(\displaystyle \;\;\;\; ≈a^2·27.617\)
Volume (\(\small{V}\))
\(\displaystyle V=\frac{25}{88}· a^3·\sqrt{6·(185+82·\sqrt{5}}\) \(\displaystyle \;\;\;\; ≈a^3·13.355\)
Midsphere radius (\(\small{R_K}\))
\(\displaystyle R_K=\frac{a}{8}·(5+3·\sqrt{5})\) \(\displaystyle \;\;\;\; ≈a·1.464\)
Insphere radius (\(\small{R_I}\))
\(\displaystyle R_I=\frac{a}{4}·\sqrt{\frac{15·(275+119·\sqrt{5}}{241}}\) \(\displaystyle \;\;\;\; ≈a·1.451\)
Triangle Size
Long edge (\(\small{a}\))
\(\displaystyle a=\frac{22·b}{3·(4+\sqrt{5})}\) \(\displaystyle \;\;\;\; ≈b·1.176\)
Medium edge (\(\small{b}\))
\(\displaystyle b=\frac{3}{22}·a·(4+\sqrt{5})\) \(\displaystyle \;\;\;\; ≈\frac{a}{1.176}\)
Short edge (\(\small{c}\))
\(\displaystyle c=\frac{5}{44}· a·(7-\sqrt{5})\) \(\displaystyle \;\;\;\; ≈\frac{a}{1.847}\)
Angle (\(\small{α }\))
\(\displaystyle cos\;\; \alpha=\frac{1}{30}·(5-2·\sqrt{5})\) \(\displaystyle \;\; ≈88°\;59'\;30''\)
Angle (\(\small{β}\))
\(\displaystyle cos\;\; \beta=\frac{1}{20}·(15-2·\sqrt{5})\) \(\displaystyle \;\; ≈58°\;14'\;17''\)
Angle (\(\small{γ}\))
\(\displaystyle cos\;\; \gamma=-\frac{1}{24}·(9+5·\sqrt{5})\) \(\displaystyle \;\; ≈32°\;46'\;13''\)
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