For any convex polyhedron, the number of vertices minus the number of edges plus the number of faces equals two. Discovered by Leonhard Euler, it is the earliest example of a topological invariant, later generalized as the Euler characteristic.
Facts
StatementFor any convex polyhedron, the number of vertices minus the number of edges plus the number of faces equals two. 1 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Named After
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Proved By
Sources
1. Euler Characteristic (Wikipedia)
Wikimedia Foundationopening paragraphs, historical background
It was stated for Platonic solids in 1537 in an unpublished manuscript by Francesco Maurolico. Leonhard Euler, for whom the concept is named, introduced it for convex polyhedra more generally but failed to rigorously prove that it is an invariant.
Polyhedra section
This equation, stated by Euler in 1758, is known as Euler's polyhedron formula.
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