Rotunda Calculation
Calculators and formulas for a rotunda (Johnson solid J6)
The rotunda has an regular decagon as its base and a regular pentagon as its top. The sides of the rotunda are bounded by 10 equilateral triangles and 5 regular pentagons. All edges have the same length. The rotunda is one of the Johnson solids (J6).
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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Rotunda Formulas
Volume (\(\small{V}\))
\(\displaystyle V= \frac{1}{12}·( 45 + 17 · 5 ) · a^3\;\;\;\;≈6.9178 ·a^3\)
Surface area (\(\small{S}\))
\(\displaystyle S= \frac{1}{2}· (5·\sqrt{3} + \sqrt{10 · ( 65 + 29·\sqrt{5})}) · a^2\) \(\displaystyle \;\;\;\;≈22.347 ·a^2\)
Height (\(\small{h}\))
\(\displaystyle h= \sqrt{1 + \frac{2}{\sqrt{5}}} · a \;\;\;\;≈1.376 ·a\)
Circumradius (\(\small{r}\))
\(\displaystyle r=\frac{1}{2} · (1 + \sqrt{5}) · a\;\;\;\;≈1.618 ·a \)
Square Pyramid • Pentagonal Pyramid • Triangular Cupola • Square Cupola • Pentagonal Cupola • Rotunda • Elongated Triangular Pyramid • Elongated Square Pyramid • Elongated Pentagonal Pyramid • Triangular Bipyramid • Pentagonal Bipyramid • Elongated Square Bipyramid • Gyrobifastigium • Gyroelongated Square Dipyramid • Snub Disphenoid
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