Antiprism calculator
Calculator and formulas for calculating an antiprism
This function calculates the volume, surface area and height of an antiprism. An antiprism is a prism whose bases are rotated to each other by 180°/n. In a regular antiprism, all side lengths are equal.
To calculate, select a property whose magnitude you know and enter its value. Then click on 'Calculate'.
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Formulas for the antiprism
Surface (\(\small{S}\))
\(\displaystyle S = \frac{n}{2} \cdot \left(cot\left(\frac{π}{n}\right) + \sqrt{3}\right) \cdot a^2 \)
Volume (\(\small{V}\))
\(\displaystyle V = \frac{ n \cdot \sqrt{ 4 \cdot cos^2\left(\frac{π}{2\cdot n}\right) -1} \cdot sin\left(\frac{3\cdot π}{2\cdot n}\right)}{12 \cdot sin^2\left(\frac{π}{n}\right)} \cdot a^3\)
Height (\(\small{h}\))
\(\displaystyle h = \sqrt{1 - \frac{1 }{cos\left(\frac{π}{2 \cdot n}\right)^2 \cdot 4}} \cdot a\)
The angle function of a calculator must be set to RAD.
Cuboid
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Square Pillar
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Antiprism
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Hexagonal prism
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Triangular prism
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Regular prism
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Oblique prism
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Ramp
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Anticube
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Wedge
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Right Wedge
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Rhombohedron
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Parallelepiped
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Tetrahedron, irregular
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Tetragonal Trapezohedron
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Pentagonal Trapezohedron
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Prismatoid
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Stellated Octahedron
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Stellated Dodecahedron
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Great Stellated Dodecahedron
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Great Dodecahedron
Tetrahedron • Cube • Octahedron • Dodecahedron • Icosahedron
Tetrahedron • Cube • Octahedron • Dodecahedron • Icosahedron
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