What is the equilibrium arrangement of the six digits on the dodecahedron?

Question

Mathematics

There is a dodecahedron, it is necessary to place numbers from 1 to 6 on its faces so that the probability of their loss is the same.

I would be glad to see either a ready-made answer right away, or an algorithm on how to come to this answer. Or at least chapter titles in probability theory that will help me figure it out.

Answer 1

Arrange as you like, as long as each number occurs exactly on two faces. It is believed that a regular polyhedron has the same probability of falling out of each face.
If you are afraid that the numbers will be of different weights and the heavier one will be at the bottom more often - place the same numbers on opposite faces. Then they balance each other out.