xvi Notation Cones Cone(S) convex cone generated by S (1) σ rational convex polyhedral cone in NR (1) Span(σ) subspace spanned by σ (1) dim σ dimension of σ (1) σ∨ dual cone of σ (1) Relint(σ) relative interior of σ (1) Int(σ) interior of σ when Span(σ) = NR (1) σ⊥ set of m ∈ MR with m,σ = 0 (1) τ σ, τ ≺ σ τ is a face or proper face of σ (1) τ ∗ face of σ∨ dual to τ ⊆ σ, equals σ∨ ∩ τ ⊥ (1) Rays ρ 1-dimensional strongly convex cone (a ray) in NR (1) uρ minimal generator of ρ ∩ N, ρ a rational ray in NR (1) σ(1) rays of a strongly convex cone σ in NR (1) Lattices ZA lattice generated by A (1) Z A elements ∑s i=1 aimi ∈ ZA with ∑s i=1 ai = 0 (2) Nσ sublattice Z(σ ∩ N) = Span(σ) ∩ N (3) N(σ) quotient lattice N/Nσ (3) M(σ) dual lattice of N(σ), equals σ⊥ ∩ M (3) Fans Σ fan in NR (2,3) Σ(r) r-dimensional cones of Σ (3) Σmax maximal cones of Σ (3) Star(σ) star of σ, a fan in N(σ) (3) Σ∗(σ) star subdivision of Σ for σ ∈ Σ (3) Σ∗(v) star subdivision of Σ for v ∈ |Σ|∩ N primitive (11) Polytopes and Polyhedra Δn standard n-simplex in Rn (2) Conv(S) convex hull of S (1) dim P dimension of a polyhedron P (2) Q P, Q ≺ P Q is a face or proper face of P (2) P◦ dual or polar of a polytope (2) A + B Minkowski sum (2) kP multiple of a polytope or polyhedron (2)

Purchased from American Mathematical Society for the exclusive use of nofirst nolast (email unknown) Copyright 2011 American Mathematical Society. Duplication prohibited. Please report unauthorized use to cust-serv@ams.org. Thank You! Your purchase supports the AMS' mission, programs, and services for the mathematical community.