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A planar quadrangulation is a planar map in which every face has degree four, with incidences counted with multiplicity. A pointed quadrangulation additionally has a distinguished vertex.

A squaregraph has separate conditions on bounded faces and interior vertex degrees; its outer face need not be quadrilateral.

A squaregraph has a plane embedding in which every bounded face has four sides and every interior vertex has degree at least four. Its outer face may have more than four sides, so this definition differs from a planar quadrangulation requiring every face to have degree four.