# The Golden Ratio in Arrangements of Octahedron, Cube, Tetrahedron, and Sphere

The Golden Ratio in Arrangements of Octahedron, Cube, Tetrahedron, and Sphere

The edge of an octahedron of length 1 and the edge of a smaller octahedron of length determine a straight line, one endpoint of which is at the face center of a matching cube, while its other endpoint is on a sphere circumscribing the cube.

1/ϕ≈0.61803…