x_{1} is pickle-/cucumber-shaped

Should be three-dimensional and enclose a volume. The shape is approximately cylindrical: there is an approximately linear, non-closed axis and any cross-section that is perpendicular thereto should be approximately circular (or trivial). The ends should be rounded and can be tapered; the should not be sharp. The shape is fairly smooth. If the axis is linear, the shape should be convex. The axis should, at most, form a shape like a parenthesis "("; there should not be multiple changes in the sign of curvature. The diameter of the perpendicular cross-section should be largest toward the middle of the axis; the length of the axis should be rather larger than this diametric length.