Octahedron Calculator

Name: Octahedron - Geometry Calculator
Author: Jürgen Kummer

Calculations at a regular octahedron, a solid with eight faces, edges of equal length and angles of equal size. The octahedron is the third of the five Platonic solids.
Enter one value and choose the number of decimal places. Then click Calculate.

Formulas:

A = 2 \cdot a^{2} \cdot \sqrt{3}

V = \frac{a^{3}}{3} \cdot \sqrt{2}

d = \sqrt{2} \cdot a (= 2 \cdot r_{U})

r_{c} = \frac{a}{2} \cdot \sqrt{2}

r_{m} = \frac{a}{2}

r_{i} = \frac{a}{6} \cdot \sqrt{6}

\frac{A}{V} = \frac{3 \cdot \sqrt{6}}{a}

The regular octahedron is a Platonic solid. Edge length, diagonal and radius have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit ^-1.

Net of an octahedron, the three-dimensional body is unfolded in two dimensions.

The dual body of the regular octahedron is the cube or regular hexahedron and vice versa. The octahedron is point-symmetrical to its center, has 9 planes of symmetry and 12 axes of rotation to which it is rotationally symmetrical. If the corners of an octahedron are regularly cut off, the Archimedean body truncated octahedron is created. The intersection of two equally sized, mutually aligned tetrahedrons is an octahedron.
There are eight-sided dices in the shape of an octahedron. Several minerals crystallize octahedrally, including alum and diamond. According to Plato, the octahedron is associated with the element air. The tetrahedron stands for fire, the cube for earth, the icosahedron for water and the dodecahedron for the celestial element ether. This doctrine of the connection of the Platonic solids with the four earthly and one celestial basic elements lasted until the early modern period and was expanded by Johannes Kepler to include the sky and the stars. More and different chemical elements are now known, and the planetary orbits are also completely different. But the regular polyhedra are still the same as in Plato's time and will not change.

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