# Euclid's Construction of a Regular Octahedron (XIII.14)

Euclid's Construction of a Regular Octahedron (XIII.14)

Let be the center of an arbitrary sphere, and be two perpendicular diameters, and be the diameter perpendicular to the plane defined by and . Then is a regular octahedron.

K

AC

BD

LM

AC

BD

LABCDM