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

step

1

2

3

4

5

transparency

Let

K

be the center of an arbitrary sphere,

AC

and

BD

be two perpendicular diameters, and

LM

be the diameter perpendicular to the plane defined by

AC

and

BD

. Then

LABCDM

is a regular octahedron.