Geodesic
Projective invariant Demazure models
Izvestiya. Mathematics , Tome 20 (1983) no. 2, pp. 189-202

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This paper gives a detailed exposition of the construction of models of tori that are not decomposable over the base field. The presence of a finite number of nonconjugate subgroups in the group $\operatorname{GL}(n,\mathbf Z)$ enables one to classify the tori of given dimension by the Bravais type of their modules of rational characters. A quite complete description of projective Demazure models in low dimensions is given. The rationality of tori with cubic character lattices is proved. Bibliography: 15 titles. 
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     author = {V. E. Voskresenskii},
     title = {Projective invariant {Demazure} models},
     journal = {Izvestiya. Mathematics },
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V. E. Voskresenskii. Projective invariant Demazure models. Izvestiya. Mathematics , Tome 20 (1983) no. 2, pp. 189-202. http://geodesic.mathdoc.fr/item/IM2_1983_20_2_a0/