dim X
The dimension of a normal toric variety equals the dimension of its dense algebraic torus. In this package, the fan associated to a normal $d$-dimensional toric variety lies in the rational vector space $\QQ^d$ with underlying lattice $N = \ZZ^d$. Hence, the dimension simply equals the number of entries in a minimal nonzero lattice point on a ray.
The following examples illustrate normal toric varieties of various dimensions.
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In this package, number of entries in any ray equals the dimension of both the underlying lattice and the normal toric variety, so this method does essentially no computation.