Geodesic
Rationality of an Enriques--Fano threefold of genus five
Izvestiya. Mathematics , Tome 68 (2004) no. 3, pp. 607-618

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We prove the rationality of a non-Gorenstein Fano threefold of Fano index one and degree eight having terminal cyclic quotient singularities and Picard group $\mathbb Z$. This threefold can be described as the quotient of a double covering of $\mathbb P^3$ ramified in a smooth quartic surface by an involution fixing eight different points. 
@article{IM2_2004_68_3_a8,
     author = {I. A. Cheltsov},
     title = {Rationality of an {Enriques--Fano} threefold of genus five},
     journal = {Izvestiya. Mathematics },
     pages = {607--618},
     publisher = {mathdoc},
     volume = {68},
     number = {3},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2004_68_3_a8/}
}
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I. A. Cheltsov. Rationality of an Enriques--Fano threefold of genus five. Izvestiya. Mathematics , Tome 68 (2004) no. 3, pp. 607-618. http://geodesic.mathdoc.fr/item/IM2_2004_68_3_a8/