Tetragonal Trapezohedron calculator and formulas

This function calculates parameters of a regular tetragonal 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'.

Tetragonal Trapezohedron

Input

Decimal places

Results

Side a

Side b

Antiprism z

Volume V

Surface S

Height h

Formulas for a tetragonal trapezohedron

Edge length antiprism \(=z\)

Side a

\(\displaystyle a = \sqrt{\sqrt{2} -1} \cdot z \;\;\;≈0.6436\cdot z\)

Side b

\(\displaystyle b = \frac{\sqrt{2 \cdot (1 + \sqrt{2})}}{2} \cdot z \;\;\;≈1.0987\cdot z\)

Height

\(\displaystyle h = \sqrt{ \frac{ 1}{2} \cdot (4 + 3 \cdot \sqrt{2})} \cdot z \;\;\;≈2.03\cdot z\)

Surface

\(\displaystyle s = 2 \cdot \sqrt{2 + 4 \cdot \sqrt{2}} \cdot z^2 \;\;\;≈5.5342\cdot z^2\)

Volume

\(\displaystyle V =\frac{1}{3} \cdot \sqrt{ 4 + 3 \cdot \sqrt{2}} \cdot z^3 \;\;\;≈ 0.957 \cdot z^3\)