To have less air resistance (in the case of rockets, while they are still in the atmosphere).
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To reduce air resistance.
pentagon
No, vertices do not have to be pointed out. Vertices are the points where the edges of a shape or object meet. They can be sharp or rounded, depending on the shape or object.
There are many options. Amongst them: An ellipsoid (including a sphere) intersected by two planes which do not, themselves intersect within the shape; A paraboloid intersected by two planes which do not, themselves intersect within the shape; A cone intersected by two planes which do not, themselves intersect within the shape; A semi-hyperboloid intersected by two planes which do not, themselves intersect within the shape; A toroid (doughnut) intersected by two planes which do not, themselves intersect within the shape; An elliptic prism intersected by two planes which do not, themselves intersect within the shape. The last of these would include a cylinder.
So it can keep it's direction