The height of the equilateral triangle is, so the portion above the circumcenter has length; this is the hypotenuse of an equilateral triangle with half of a diagonal of the cube as the longer leg, and the shorter leg is of the height of the pyramid, or . Therefore, each side of the cube has length . Therefore, the volume of the cube is, and the volume of the octahedron is, and the ratio of the volumes is .
Ang taas ng equilateral triangle ay, Kaya ang mga bahagi sa itaas ng circumcenter ay may haba; Ito ay ang hypotenuse ng isang equilateral triangle sa kalahati ng isang dayagonal ng kubo bilang na paa, at ang mas maiksi paa ay sa taas ng piramide, o . Samakatuwid, ang bawat bahagi ng kubo ay may haba . Kaya, ang lakas ng tunog ng kubo ay, At ang lakas ng tunog ng octahedron ay, At ang ratio ng volume ay .