Equations for the torus

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\begin{align*}a &= \text{ distance from $z$-axis}=R+r\cos(\phi) \\ x &= a\cos(\theta) \\ y &= a\sin(\theta) \end{align*} \begin{align*}x &= (R+r\cos(\phi))\cos(\theta) \\ y &= (R+r\cos(\phi))\sin(\theta) \\ z &= r\sin(\phi) \end{align*} \begin{align*}a &= \text{ distance from $z$-axis}=R+r\cos(\phi) \\ z &= r\sin(\phi) \end{align*}