Pentagonal Icositetrahedron
Calculators and formulas for the pentagonal icositetrahedron
This function calculates various parameters of a pentagonal icositetrahedron. Entering one value is sufficient for the calculation; all others are calculated from it.
The pentagonicositetrahedron is a polyhedron composed of 24 irregular pentagons. It is dual to the chamfered hexahedron and has 38 vertices and 60 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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Pentagonal Icositetrahedron Formulas
Tribonacci constant (\(\small{t}\)) und (\(\small{s}\))
\(\displaystyle t ≈ 1.839286755214161 \)
\(\displaystyle s = ( t - 1 ) / 2 = 0.41964337760708 \)
Long edge (\(\small{a}\))
\(\displaystyle a=b·(s+1)\)
Short edge (\(\small{b}\))
\(\displaystyle b=\frac{a}{s+1}\)
Surface (\(\small{S}\))
\(\displaystyle S=\frac{24·a^2·(2+3·s)}{1+2·s}\) \(\displaystyle · \sqrt{\frac{1-s}{1+s}}\)
Volume (\(\small{V}\))
\(\displaystyle V=\frac{4·a^3·(2+3·s)·\sqrt{1-2·s}}{(1+s)·(1-4·s^2)}\)
Midsphere radius (\(\small{R_K}\))
\(\displaystyle R_K=\frac{a}{\sqrt{2·(1+s)·(1-2·s)}}\)
Insphere radius (\(\small{R_I}\))
\(\displaystyle =\frac{a}{2·\sqrt{(1-2·s)·(1-s^2)}}\)
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