In a similar manner, four covertical equilateral triangles stand on a square base.
If the faces be all equal equilateral triangles the solid is termed the "regular" tetrahedron.
Five equilateral triangles covertically placed would stand on a pentagonal base, and it was found that, by forming several sets of such pyramids, a solid could be obtained which had zo triangular faces, which met in pairs to form 30 edges, and in fives to form 12 vertices.
The base of the equilateral triangle is the top of the wedge.
The regular octahedron has for its faces equilateral triangles; it is the reciprocal of the cube.