---
tag: NNZV4614R1
kind: statement
role: theorem
name: Koebe–Andreev–Thurston circle packing theorem
sources:
  - wikipedia: en:16648043@r1375504925
    locator: Circle packing theorem, section Theorem statement and proofs
    note: adopted
    mention: wikipedia://en/16648043#8YFQ
    sections: [Statement]
inventory: [Y1W9WYWMQD]
---

## Statement

If $G$ is a finite connected planar graph, then a circle packing in the plane whose tangency graph is isomorphic to $G$ exists. If $G$ has a fixed planar embedding, the circle packing can be chosen so that the cyclic order of tangencies around each circle corresponds to the order of edges around each vertex in the embedding. If $G$ is maximal planar, this packing is unique, up to reflections in lines and [[Möbius transformations|0B346DDAM5]].