sentence: the n - dimensional cross-polytope can also be defined as the closed unit ball ( or , according to some authors , its boundary ) in the -norm on r n : in 1 dimension the cross-polytope is simply the line segment ( 1 , +1 ) , in 2 dimensions it is a square ( or diamond ) with vertices -lcb- ( ± 1 , 0 ) , ( 0 , ± 1 ) -rcb- .