Gyroelongated Square Dipyramid Calculation

The sides of the gyroelongated square dipyramid are bounded by 16 equilateral triangles. All edges have the same length. This dipyramid is one of the Johnson solids (J₁₇).

To perform the calculation select the property you know from the menu and enter its value. Then click on the 'Calculate' button.

Dipyramid Calculator  Input Delete Entry Edge length Volume Surface area Height Decimal places 0 1 2 3 4 6   Resultate Edge length a Volume V Surface area S Height h

Formulas for gyroelongated square dipyramids

Volume

\(\displaystyle V= \frac{(\sqrt{2} + \sqrt{ 4 + 3 · \sqrt{2}})}{3} ·a^3\) \(\displaystyle \;\;\;\;≈ 1.4284 ·a^3\)

Surface area

\(\displaystyle S= 4 · \sqrt{3} · a^2\;\;\;\;≈ 6.9282 ·a^2\)

Height

\(\displaystyle h=\left( \sqrt{1 - \frac{1}{(2+\sqrt{2})}} + \frac{2}{\sqrt{2}} \right) · a \) \(\displaystyle \;\;\;\;≈2.255 ·a \)