Pentagonal Trapezohedron calculator and formulas

This function calculates parameters of a regular pentagonal trapezohedron. A trapezohedron (or deltoeder) is a twisted double pyramid by (180°/n) .

To calculate, select a property whose magnitude you know and enter its value. Then click on 'Calculate'.

Pentagonal Trapezohedron

Input

Decimal places

Results

Edge a

Edge b

Antiprism z

Volume V

Surface S

Height h

Formulas for a pentagonal trapezohedron

Edge length antiprism \(= z\)

Edge a

\(\displaystyle a = \frac{\sqrt{5}-1}{2}\cdot z \;\;\;≈0.618\cdot z\)

Edge b

\(\displaystyle b = \frac{\sqrt{5} + 1 }{ 2} \cdot z \;\;\;≈1.618\cdot z\)

Height

\(\displaystyle h = \sqrt{5 + 2 \cdot \sqrt{5}} \cdot z \;\;\;≈3.078\cdot z\)

Surface

\(\displaystyle S = \sqrt{\frac{25}{2} \cdot (5+\sqrt{5} )} \cdot z^2 \;\;\;≈9.51\cdot z^2\)

Volume

\(\displaystyle V =\frac{5}{12} \cdot (3 + \sqrt{5} ) \cdot z^3 \;\;\;≈ 2.1817 \cdot z^3\)