Count faces, edges and vertices of any solid with flat faces and no holes, then work out F − E + V. You always get 2.

• Cube: 6 − 12 + 8 = 2
• Square pyramid: 5 − 8 + 5 = 2
• Tetrahedron: 4 − 6 + 4 = 2

Leonhard Euler wrote this down in 1750. It is one of the first results of topology, the maths of shape without measurement.