Pentagonal Trapezohedron Calculation
Calculator and formulas for a pentagonal trapezohedron
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'.
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Formulas for the trapezohedron
Antiprism length \(= z\)
Edge length (\(\small{a}\))
\(\displaystyle a = \frac{\sqrt{5}-1}{2}\cdot z \;\;\;≈0.618\cdot z\)
Edge length (\(\small{b}\))
\(\displaystyle b = \frac{\sqrt{5} + 1 }{ 2} \cdot z \;\;\;≈1.618\cdot z\)
Height (\(\small{h}\))
\(\displaystyle h = \sqrt{5 + 2 \cdot \sqrt{5}} \cdot z \;\;\;≈3.078\cdot z\)
Surface (\(\small{S}\))
\(\displaystyle S = \sqrt{\frac{25}{2} \cdot (5+\sqrt{5} )} \cdot z^2 \;\;\;≈9.51\cdot z^2\)
Volume (\(\small{V}\))
\(\displaystyle V =\frac{5}{12} \cdot (3 + \sqrt{5} ) \cdot z^3 \;\;\;≈ 2.1817 \cdot z^3\)
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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