Three tetrahedra and a pyramid
Four solids of the same volume, the regular tetrahedron with side , a quarter-octahedron tetrahedron made up of two equilateral triangles with side and a square folded at right angles according to the unit hypotenuse, and the twenty-fourth cube, composed of a half square of unit hypotenuse, of a height placed at the applomb of the corner, and the pyramid with a square base of side and of the same length, the apex at the applomb of a corner.
Prove analytically, or using Cavalieri's principle, that these three solids have the same volume.