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I would call it a thickened torus. I don't know how standard that is, but it is quite normal to speak of thickened manifolds, where one means a regular neighbourhood of that manifold times a closed interval.
I have long felt that there should be a mathematical dictionary- not an encyclopaedia, by a dictionary- in order to fix and record standard usage.

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I would call it a thickened torus. I don't know how standard that is, but it is quite normal to speak of thickened manifolds, where one means a regular neighbourhood of that manifold.
I have long felt that there should be a mathematical dictionary- not an encyclopaedia, by a dictionary- in order to fix and record standard usage.