MathDB

Given a regular dodecahedron of side

a

. Take two pairs of opposite faces:

E, E'

and

F, F'

. For the pair

E, E'

take the line joining the centers of the faces and take points

A

and

C

on the line each a distance

m

outside one of the faces. Similarly, take

B

and

D

on the line joining the centers of

F, F'

each a distance

m

outside one of the faces. Show that

ABCD

is a rectangle and find the ratio of its side lengths.

Problem Statement