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 *ℚ ^{d}* with underlying lattice

The general method for creating a 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
- toricProjectiveSpace(ZZ) -- make a projective space
- weightedProjectiveSpace(List) -- make a weighted projective space
- hirzebruchSurface(ZZ) -- make a Hirzebruch surface
- kleinschmidt(ZZ,List) -- make a smooth normal toric variety with Picard rank two
- NormalToricVariety ** NormalToricVariety -- make the Cartesian product of 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.