Deltoidal Hexecontahedron
Calculator and formulas for the deltoidal hexecontahedron
This function calculates various parameters of a deltoidal hexecontahedron. Entering one value is sufficient for the calculation; all others are calculated from it.
The deltoidal hexacontahedron is a convex polyhedron composed of 60 deltoids. It is dual to the rhombicicosidodecahedron and has 62 vertices and 120 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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Formeln zum Deltoidalhexakontaeder
Surface (\(\small{S}\))
\(\displaystyle S=\frac{9}{11}· a^2·\sqrt{10·(157+31·\sqrt{5})}\) \(\displaystyle \;\;\;\; ≈a^2·38.92\)
Volume (\(\small{V}\))
\(\displaystyle V=\frac{45}{11}· a^3·\sqrt{\frac{370+164·\sqrt{5}}{25}}\) \(\displaystyle \;\;\;\; ≈a^3·22.21\)
Midsphere radius (\(\small{R_K}\))
\(\displaystyle R_K=\frac{3}{20}· a·(5+3·\sqrt{5})\) \(\displaystyle \;\;\;\; ≈a·1.756\)
Insphere radius (\(\small{R_I}\))
\(\displaystyle R_I=\frac{3}{2}· a·\sqrt{\frac{135+59·\sqrt{5}}{205}}\) \(\displaystyle \;\;\;\; ≈a·1.712\)
Größen des Drachenvierecks
Long edge (\(\small{a}\))
\(\displaystyle a=\frac{22·b}{3·(7-\sqrt{5})}\) \(\displaystyle \;\;\;\; ≈b·1.54\)
Short edge (\(\small{b}\))
\(\displaystyle b=\frac{3· a·(7-\sqrt{5})}{22}\) \(\displaystyle \;\;\;\; ≈\frac{a}{1.54}\)
Short diagonal (\(\small{e}\))
\(\displaystyle e= 3·a ·\sqrt{\frac{5-\sqrt{5}}{20}}\) \(\displaystyle \;\;\;\; ≈a· 1.115\)
Long diagonal (\(\small{f}\))
\(\displaystyle f=\frac{a}{11} ·\sqrt{\frac{470+156·\sqrt{5}}{5}}\) \(\displaystyle \;\;\;\; ≈a· 1.163\)
Side angle (\(\small{\alpha}\))
\(\displaystyle cos\;\; \alpha=\frac{1}{10}·(5-2·\sqrt{5})\) \(\displaystyle \;\; ≈86°\;58'\;27''\)
Base angle (\(\small{\beta}\))
\(\displaystyle cos\;\; \beta=\frac{1}{40}·(9·\sqrt{5}-5)\) \(\displaystyle \;\; ≈67°\;46'\;59''\)
Head angle (\(\small{\gamma}\))
\(\displaystyle cos\;\; \gamma=-\frac{1}{20}·(5+2·\sqrt{5})\) \(\displaystyle \;\; ≈118°\;16'\;7''\)
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