What is a toric lattice? and how can I construct one in `Macaulay2` and compute its basis? is there any alternative method to make one? Since I went through the whole documentation of the M2 but could not find anything. For example, we know that a toric lattice of $\dim=3$ is an identity matrix of size 3.



What is a toric lattice?
From the [documentation](https://faculty.math.illinois.edu/Macaulay2/doc/Macaulay2-1.15/share/doc/Macaulay2/NormalToricVarieties/html/_normal__Toric__Variety_lp__List_cm__List_rp.html) of the `normalToricVariety(*,*)` routine (emphasis mine):



> 
> This is the general method for constructing a normal toric variety.
> 
> 
> 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
> $\mathbb{Q}^d$ with underlying lattice $N = \mathbb{Z}^d$**. The fan is encoded by the minimal
> nonzero lattice points on its rays and the set of rays defining the
> maximal cones (meaning cones that are not proper subsets of another
> cone in the fan). More precisely, `rayList` lists the minimal nonzero
> lattice points on each ray (a.k.a. one-dimensional cone) in the fan.
> Each lattice point is a list of integers. The rays are ordered and
> indexed by nonnegative integers: $0,1,\dotsc,n$. Using this indexing, a
> maximal cone in the fan corresponds to a sublist of $\{0,1,\dotsc,n\}$. All
> maximal cones are listed in `coneList`.
> 
> 
> 


I'd imagine the other routines either take the same approach or explain it in their documentation.


