Tetragonal Trapezohedron Calculation
Calculator and formulas for a tetragonal trapezohedron
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'.
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Trapezohedron formulas
Length of the antiprism \(= z\)
Side length (\(\small{a}\))
\(\displaystyle a = \sqrt{\sqrt{2} -1} \cdot z \;\;\;≈0.6436\cdot z\)
Side length (\(\small{b}\))
\(\displaystyle b = \frac{\sqrt{2 \cdot (1 + \sqrt{2})}}{2} \cdot z \;\;\;≈1.0987\cdot z\)
Height (\(\small{b}\))
\(\displaystyle h = \sqrt{ \frac{ 1}{2} \cdot (4 + 3 \cdot \sqrt{2})} \cdot z \;\;\;≈2.03\cdot z\)
Surface (\(\small{S}\))
\(\displaystyle S = 2 \cdot \sqrt{2 + 4 \cdot \sqrt{2}} \cdot z^2 \;\;\;≈5.5342\cdot z^2\)
Volume (\(\small{V}\))
\(\displaystyle V =\frac{1}{3} \cdot \sqrt{ 4 + 3 \cdot \sqrt{2}} \cdot z^3 \;\;\;≈ 0.957 \cdot z^3\)
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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