To find the volume of an octahedron, it is enough to remember one simple formula in which there is only one unknown quantity. But first, let’s remember what each word of the designated concept describes.
Formulas and definitions
Volume (from lat. volume–”filling”) is a quantitative characteristic of the space occupied by a body or substance.
Octahedron (from Greek. – “eight bases”) is a polyhedron (polyhedron) with eight faces.
A regular octahedron is one of the 5 “Platonic solids”, i.e. regular polyhedra. Its faces are equilateral (regular) triangles (in the amount of 8 pieces). It also has 12 edges and 6 vertices (in each of which 4 edges converge).
The formulas for calculating the octahedron volume are as follows:
where a is the edge length of the polyhedron in question.