Equations · equation
Euler's Polyhedron Formula
Vectors & Geometry · 1752
- Equation
- V − E + F = 2
- Field
- Vectors & Geometry
- Named After
- Leonhard Euler
- Symbols
- V, E, F the numbers of vertices, edges and faces of any convex polyhedron
- Year
- 1752
Significance
Count the corners, edges and faces of a cube (8, 12, 6), a tetrahedron (4, 6, 4) or a soccer ball (60, 90, 32) and the same 2 comes out every time. It does not care about lengths or angles — only how the pieces connect — which made it the first theorem of topology. It is why there are exactly five Platonic solids, and it constrains every crystal habit on the minerals page: a form's faces and edges must obey it.
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