Abstract

We study the mirror geometry of the blow-up of the affine 4 singularity by using a special tetravalent geometry based on an irreducible tetravalent vertex. The latter is a toric geometry of polytopes of the cubic half-integer lattice. Our construction allows us to derive a new representation of the affine n geometries including the special 4 case. Comments on the various types of irreducible and reducible tetravalent vertices are also made.

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