A normal toric variety corresponds to a strongly convex rational polyhedral fan in affine space. In this package, the fan associated to a normal $d$-dimensional toric variety lies in the rational vector space $\QQ^d$ with underlying lattice $N = \ZZ^d$. The fan is encoded by the minimal nonzero lattice points on its rays and the set of rays defining the maximal cones (a maximal cone is not properly contained in another cone in the fan). More information about the correspondence between normal toric varieties and strongly convex rational polyhedral fans appears in Subsection 3.1 of Cox-Little-Schenck.

The general method for creating normal toric variety is normalToricVariety. However, there are many additional methods for constructing other specific types of normal toric varieties.

- normalToricVariety(List,List) -- make a normal toric variety
- normalToricVariety(Matrix) -- make a normal toric variety from a polytope
- NormalToricVariety -- the class of all normal toric varieties
- isWellDefined(NormalToricVariety) -- whether a toric variety is well-defined
- affineSpace(ZZ) -- make an affine space as a normal toric variety
- projective space -- information about various constructions of projective space
- toricProjectiveSpace(ZZ) -- make a projective space as a normal toric variety
- weightedProjectiveSpace(List) -- make a weighted projective space
- hirzebruchSurface(ZZ) -- make any Hirzebruch surface
- kleinschmidt(ZZ,List) -- make any smooth normal toric variety having Picard rank two
- NormalToricVariety ** NormalToricVariety -- make the Cartesian product of two normal toric varieties
- NormalToricVariety ^** ZZ -- make the Cartesian power of a normal toric variety
- smoothFanoToricVariety(ZZ,ZZ) -- get a smooth Fano toric variety from database
- normalToricVariety(Fan) -- make a normal toric variety from a 'Polyhedra' fan
- normalToricVariety(Polyhedron) -- make a normal toric variety from a 'Polyhedra' polyhedron

Several methods for making new normal toric varieties from old ones are listed in the section on resolution of singularities.

- finding attributes and properties -- information about accessing features of a normal toric variety
- resolving singularities -- information about find a smooth proper birational surjection
- working with toric maps -- information about toric maps and the induced operations
- working with divisors -- information about toric divisors and their related groups
- working with sheaves -- information about coherent sheaves and total coordinate rings (a.k.a. Cox rings)