Deltoidal Icositetrahedron
Calculators and formulas for deltoidal icositetrahedron (also a trapezoidal icositetrahedron)"
This function calculates various parameters of a deltoidal icositetrahedron (also a trapezoidal icositetrahedron). Entering one value is sufficient for the calculation; all others are calculated from it.
The deltoidal icositetraeder is a polyhedron with 24 faces, where these faces are congruent deltoids. It has 26 corners and 48 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 Deltoidalikositetraeder
Long edge (\(\small{a}\))
\(\displaystyle a=\frac{7·b}{4+\sqrt{2}}\) \(\displaystyle ≈\frac{7·b}{5.41}\)
Short edge (\(\small{b}\))
\(\displaystyle b=\frac{a·(4+\sqrt{2})}{7}\) \(\displaystyle ≈\frac{a·5.41}{7}\)
Diagonal (\(\small{e}\))
\(\displaystyle e=\frac{a·\sqrt{46+15·\sqrt{2}}}{7}\) \(\displaystyle ≈\frac{a·8.2}{7}\)
Diagonal (\(\small{f}\))
\(\displaystyle e=\frac{a·\sqrt{4+2·\sqrt{2}}}{2}\) \(\displaystyle ≈\frac{a·2.613}{2}\)
Surface (\(\small{S}\))
\(\displaystyle S=\frac{12·a^2·\sqrt{61+38·\sqrt{2}}}{7}\) \(\displaystyle ≈\frac{a^2·128.54}{7}\)
Volume (\(\small{V}\))
\(\displaystyle V=\frac{2·a^3·\sqrt{292+206·\sqrt{2}}}{7}\) \(\displaystyle ≈\frac{a^3·48.30}{7}\)
Midsphere radius (\(\small{R_K}\))
\(\displaystyle R_K=\frac{a·(1+\sqrt{2})}{2}\) \(\displaystyle ≈\frac{a·2.41}{2}\)
Insphere radius (\(\small{R_I}\))
\(\displaystyle R_I=a·\sqrt{\frac{22+15·\sqrt{2}}{34}}\) \(\displaystyle ≈a·1.1273\)
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