Saved on this device

Follow your curiosity

What discovery has been shared with you?

FACTREE gives you something interesting to discover every day — and something worth talking about together.

Start with one fact. Explore it, go deeper, then follow whichever branch catches your imagination.

Choose subjects for a surprise

Exploring any topic

Begin your discovery

Your next discovery is one click away.

Choose one or more subjects above, or leave Any Topic selected and let curiosity decide.

Mathematics

The Euler Characteristic and the Topology of Polyhedra

Quick fact

For any convex polyhedron, the number of vertices minus the number of edges plus the number of faces always equals 2. This holds for a cube (8 - 12 + 6), a tetrahedron (4 - 6 + 4), and even a soccer ball (60 - 90 + 32).

Why this is interesting

You've probably noticed that cubes and pyramids look quite different, but what if a mathematician told you they share a hidden, deeper connection? What is it that these shapes have in common that makes them fundamentally the same to a topologist?