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Hal Schenck coauthored a text on toric varieties with David A. Cox and John B. Little. It develops the bridge between the geometry of polyhedra and algebraic geometry, including the construction of varieties from a fan in toric geometry and the study of their divisors and line bundles. Combinatorial data thereby become tools for geometric calculations.^[ref]

John B. Little coauthored a text on toric varieties with David A. Cox and Hal Schenck. Its organizing idea is that cones, a fan in toric geometry and lattice data describe substantial parts of the geometry. This provides explicit examples and calculations for algebraic varieties that can otherwise be difficult to visualize or compute with.^[ref]

By David A. Cox, John B. Little and Hal Schenck. American Mathematical Society, 2011. Author book page: dacox.people.amherst.edu/toric.html . Consulted draft: web.ma.utexas.edu/users/ikmartin/pages/additional-pages/toric-page/documents/Toric-Varieties_Cox-Little-Schenck.pdf . Chapters 1–3 give cones, normal toric varieties and orbits; chapters 4–6 treat divisors, homogeneous coordinates and line bundles.