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ball, cube and cylinder. – A mathematical object is an abstract object arising in philosophy of mathematics and mathematics itself. Commonly encountered mathematical objects include numbers, permutations, partitions, matrices, sets, functions, and relations. Geometry as a branch of mathematics has such objects as hexagons, points, lines, triangles, circles, spheres, polyhedra, ... Another branch – algebra – has groups, rings, fields, group-theoretic lattices, and order-theoretic lattices.