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A Rugby ball
No shape is mathematical really unless it has been created by a mathematical formula, but is certainly a geometric shape. But anything which is a 2D or 3D shape is geometric. My improvement: A catenary curve from a mathematical equation such as cosh x, is a mathematical and natural shape. Maby each other arch can be approximated by a mathematical formula.
The term prism describes the shape of a wedge. It looks like a triangle on the two ends.
There is no specific name. There are spheres, ellipsoids, paraboloids, etc. Then there are 3-d cycloids,
Any shape is mathematical.