Volume formula

A regular octahedron has 8 congruent triangular faces, 12 edges, and 6 vertices.

Its volume follows V= rac{sqrt{2}}{3}a^3, where aa is the common edge length.

Because the edge is cubed, small size changes create much larger volume changes.

Reading the solid

  • The regular octahedron can be split into two equal square pyramids.
  • Each face is an equilateral triangle with area rac{sqrt{3}}{4}a^2.
  • It is one of the five Platonic solids.