A rugby ball is, mathematically speaking, a "prolate spheroid"spheroid-1By the way, the mathematical name of the shape of a coffee grain is "Remb's surface"http://mathworld.wolfram.com/RembsSurface.html
The shape of a soccer ball is a sphere. The stitching pattern of a traditional ball is that of a truncated icosahedron cocentric with the sphere with the pattern projected onto the sphere.
To the best of my knowledge it would simply be described as a polygon. I believe the specific name is a truncated icosahedron.
A soccer ball got its name from England i am pretty sure.
The shape of a tin can is a cylinder.
The name for a solid shape made out of that specific arrangement of hexagons and pentagons is known as a 'truncated icosohedron'. Once fully inflated, a ball is typically spherical in shape. So the geometric name would be a sphere.