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This is the first one of a series of papers on association of orientations,lattice polytopes, and abelian group arrangements to graphs. The purpose is tointerpret the integral and modular tension polynomials of graphs at zero andnegative integers. The whole exposition is put under the framework of subgrouparrangements and the application of Ehrhart polynomials. Such viewpoint leadsto the following main results of the paper: (i) the reciprocity law forintegral tension polynomials; (ii) the reciprocity law for modular tensionpolynomials; and (iii) a new interpretation for the value of the Tuttepolynomial $T(G;x,y)$ of a graph $G$ at $(1,0)$ as the number ofcut-equivalence classes of acyclic orientations on $G$.

Orientations, lattice polytopes, and group arrangements I: Chromatic and tension polynomials of graphs