Antiprism calculator and formula

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'.

Cube calculator

Input

Number of vertices

Decimal places

Results

Side a

Volume V

Surface S

Height h

Formulas for calculating an antprism

Surface

\(\displaystyle S = \frac{n}{2} \cdot \left(cot\left(\frac{π}{n}\right) + \sqrt{3}\right) \cdot a^2 \)

Volume

\(\displaystyle V = \frac{ n \cdot \sqrt{ 4 \cdot cos^2\left(\frac{π}{2\cdot n}\right) -1} \cdot sin\left(\frac{3\cdot π}{2\cdot n}\right)}{12 \cdot sin^2\left(\frac{π}{n}\right)} \cdot a^3\)

Height

\(\displaystyle h = \sqrt{1 - \frac{1 }{cos\left(\frac{π}{2 \cdot n}\right)^2 \cdot 4}} \cdot a\)

The angle function of the calculator must be set to RAD.

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