This is a Stewart Toroid. For a defintion, see the Wikipedia entry at
https://en.wikipedia.org/wiki/Toroidal_polyhedron, or better still, if you can get hold of a copy,
Adventures Among the Toroids, by B. M. Stewart. Unfortunately Professor Stewart did not live long enough for 3D printing to become available to make solid versions of his toroids. I am an admirer of his work and i am working on making some of his toroids available on solid form. This is the simplest one with a three-dimansional symmetry group. If there is enough interest I will try to model some of his more complex toroids. This is a version suitable for display. I can make different sizes available on request. There is also a smaller version with a hanging loop attached, suitable for printing in silver or gold as an earring or a pendant. There is a more complex Stewart Toroid at
https://www.shapeways.com/product/G2XNXYGJY/k4-12p4-e4?optionId=335102755
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