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Note that with the normal definition of power the above equations are only defined for a single quadrant, namely that where the cosine and sine terms are positive. When creating the supertorus in practice one has two choices, either replicate the result in the one quadrant to the other three with the correct mirror operations, or define xn = sign(x) * abs(x)n.
But of course... Using the Way Back machine, it used to read differently:
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It is different values of these powers which give rise to a family of 3D shapes all basically toroidal in shape. The value of n1 determines the shape of the torus ring, n2 determines the shape of the cross section of the ring.
Examples of the supertoroid generated for different values of n1 and n2 are shown below, of course, the legal values of n1 and n2 form a continuum of values from 0 to infinity (although there are representation issues near 0 and above 4).