Disdyakis Triacontahedron calculator and formulas

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.

Disdyakis triacontahedron calculator

Input

Argument type

Argument value

Decimal places

Results

Long edge a

Medium edge b

Short edge c

Surface A

Volume V

Midsphere radius R_K

Insphere radius R_I

Disdyakis triacontahedron formulas

Surface

\(\displaystyle A=\frac{15}{44}· a^2·\sqrt{10·(417+107·\sqrt{5})}\) \(\displaystyle \;\;\;\; ≈a^2·27.617\)

Volume

\(\displaystyle V=\frac{25}{88}· a^3·\sqrt{6·(185+82·\sqrt{5}}\) \(\displaystyle \;\;\;\; ≈a^3·13.355\)

Midsphere radius

\(\displaystyle R_K=\frac{a}{8}·(5+3·\sqrt{5})\) \(\displaystyle \;\;\;\; ≈a·1.464\)

Insphere radius

\(\displaystyle R_I=\frac{a}{4}·\sqrt{\frac{15·(275+119·\sqrt{5}}{241}}\) \(\displaystyle \;\;\;\; ≈a·1.451\)

Sizes of the triangle

Long edge

\(\displaystyle a=\frac{22·b}{3·(4+\sqrt{5})}\) \(\displaystyle \;\;\;\; ≈b·1.176\)

Medium edge

\(\displaystyle b=\frac{3}{22}·a·(4+\sqrt{5})\) \(\displaystyle \;\;\;\; ≈\frac{a}{1.176}\)

Short edge

\(\displaystyle c=\frac{5}{44}· a·(7-\sqrt{5})\) \(\displaystyle \;\;\;\; ≈\frac{a}{1.847}\)

Angle α

\(\displaystyle cos\;\; \alpha=\frac{1}{30}·(5-2·\sqrt{5})\) \(\displaystyle \;\; ≈88°\;59'\;30''\)

Angle β

\(\displaystyle cos\;\; \beta=\frac{1}{20}·(15-2·\sqrt{5})\) \(\displaystyle \;\; ≈58°\;14'\;17''\)

Angle γ

\(\displaystyle cos\;\; \gamma=-\frac{1}{24}·(9+5·\sqrt{5})\) \(\displaystyle \;\; ≈32°\;46'\;13''\)

Disdyakis Triacontahedron

Calculate the disdyakis triacontahedron

Disdyakis triacontahedron formulas

Sizes of the triangle

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