Having made a NormalToricVariety one can access its basic invariants or test for some elementary properties by using the following methods:

- rays(NormalToricVariety) -- get the rays of the associated fan
- max(NormalToricVariety) -- get the maximal cones in the associated fan
- expression(NormalToricVariety) -- get the expression used to format for printing
- dim(NormalToricVariety) -- get the dimension of a normal toric variety
- orbits(NormalToricVariety,ZZ) -- get a list of the torus orbits (a.k.a. cones in the fan) of a given dimension
- isDegenerate(NormalToricVariety) -- whether a toric variety is degenerate
- isSimplicial(NormalToricVariety) -- whether a normal toric variety is simplicial
- isSmooth(NormalToricVariety) -- whether a normal toric variety is smooth
- isComplete(NormalToricVariety) -- whether a toric variety is complete
- isProjective(NormalToricVariety) -- whether a toric variety is projective
- isFano(NormalToricVariety) -- whether a normal toric variety is Fano
- fan(NormalToricVariety) -- make the 'Polyhedra' fan associated to the normal toric variety