Geodesic
Toroidal Fano varieties and root systems
Izvestiya. Mathematics , Tome 24 (1985) no. 2, pp. 221-244.

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In this paper it is shown that over an algebraically closed field there exist only finitely many mutually nonisomorphic toroidal Fano varieties. We give a complete description of toroidal Fano varieties with a centrally symmetric fan. We prove the rationality of a special class of toroidal Fano varieties and consider applications to problems of rationality of algebraic groups. Bibliography: 17 titles. 
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V. E. Voskresenskii; A. A. Klyachko. Toroidal Fano varieties and root systems. Izvestiya. Mathematics , Tome 24 (1985) no. 2, pp. 221-244. http://geodesic.mathdoc.fr/item/IM2_1985_24_2_a1/

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