Calculations at a regular tetrahedron, a solid with four faces, edges of equal length and angles of equal size. See also general tetrahedron.
Enter one value and choose the number of decimal places. Then click Calculate.
Formulas:
h = a / 3 * √6
A = a² * √3
V = a³ / 12 * √2
rc = a / 4 * √6
rm = a / 4 * √2
ri = a / 12 * √6
A/V = 6 * √6 / a
The regular tetrahedron is a Platonic solid. Edge length, height 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 a tetrahedron, the three-dimensional body is unfolded in two dimensions.
The Platonic solids, of which the regular tetrahedron is the simplest, are those convex polyhedra that have the highest regularity. They all have the same regular polygons as a side surface and the same angles in each corner. Plato described them in detail in the Timaeus, but was not the discoverer. There are only 5 Platonic solids in total. In addition to the tetrahedron, these are the cube or hexahedron, octahedron, dodecahedron and icosahedron, ordered according to the number of sides that give them their name. Like the tetrahedron, octahedron and icosahedron have equilateral triangles as faces, the cube has squares and the dodecahedron has regular pentagons.
The tetrahedron is dual to itself, that is, its dual body is again a tetrahedron. A dual body is created when the corners and edges of a polyhedron are swapped. The dual tetrahedron is upside down compared to the original one. When the original and dual tetrahedrons are combined together, a stellated octahedron is created.
The Platonic solids were associated, in their usual order, with the five elements fire, earth, air, aether and water. Johannes Kepler interprets it into the solar system; the tetrahedron is the second shape from the outside after the cube.
