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In mathematics, a solid torus is a topological space homeomorphic to  , i.e. the cartesian product of the circle with a two dimensional disc endowed with the product topology. The solid torus is a connected, compact, orientable 3-dimensional manifold with boundary. The boundary is homeomorphic to  , the ordinary torus.
A standard way to picture a solid torus is as a toroid, embedded in 3-space.
Since the disk D2 is contractible, the solid torus has the homotopy type of S1. Therefore the fundamental group and simplicial homology groups are isomorphic to those of the circle:
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