The ring torus is one way to embed this space into Euclidean space, but another way to do this is the Cartesian product of the embedding of S1 in the plane with itself. This produces a geometric object called the Clifford torus, a surface in 4-space. In the field of topology, a torus is any topological space that is homeomorphic to a torus. The surface of a coffee cup and a doughnut are both topological tori with genus one. An example of a torus can be constructed by taking a rectangular strip of flexible material, for example, a rubber sheet, and joining the top edge to the bottom edge, and the left edge to the right edge, without any half-twists (compare Möbius strip). Geometry
A torus can be defined parametrically by:
where

θ, φ are angles which make a full circle, so their values start and end at the same point,
R is the distance from the center of the tube to the center of the torus,
r is the radius of the tube.Angle θ represents rotation around the tube, whereas φ represents rotation around the torus axis of revolution. R is known as the "major radius" and r is known as the "minor radius". The ratio R divided by r is known as the "aspect ratio". The typical doughnut confectionery has an aspect ratio of about 3 to 2.
For example, in the following map:

  
    
      
        (
        x
        ,
        y
        ,
        z
        )
        =
        (
        (
        R
        +
        P
        sin
        ⁡
        v
        )
        cos
        ⁡
        u
        ,
        (
        R
        +
        P
        sin
        ⁡
        v
        )
        sin
        ⁡
        u
        ,
        P
        cos
        ⁡
        v
        )
        .