This Demonstration shows a tetrahedron or octahedron made with similar but noncongruent triangles. With the tetrahedron, for a given root
, two triangles have sides
and two have sides
. The root is bounded by the golden ratio and its reciprocal:
. The octahedron has four of each triangle, with
and its reciprocal bounding the root. Edges are labeled with the appropriate power of the root.