Gyrobifastigium Calculation

The sides of the gyrobifastigium are bounded by four squares and four equilateral triangles. All edges have the same length. The pentagonal cupola is one of the Johnson solids (J₂₆).

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

Gyrobifastigium 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 Circumradius r

Formulas for the Gyrobifastigium

Volume

\(\displaystyle V=\frac{\sqrt{3}}{2} ·a^3 \;\;\;\;≈ 0.866 ·a^3\)

Surface area

\(\displaystyle S=(4 + \sqrt{3}) · a^2\;\;\;\;≈ 5.732 ·a^2\)

Height

\(\displaystyle h=\sqrt{3} · a\;\;\;\;≈1.732 ·a \)