For ten points, identify this shape which has a hole in it, and is the inspiration for the common saying that topologists can't tell a co ee mug from a donut.
This shape can be described in Cartesian coordinates by the equation   2 2 2 2 2c− x +y +z = a . This shape names a class of knots including thetrefoil knot and the Solomon's seal knot. This shape comes in ring, spindle, and horn varieties, and   Villarceau circles are located on this shape. This shape can be constructed from a rectangle by gluing opposite sides together without twists, and consistent with the Heawood conjecture, it requires seven colors to color every map on it. For ten points, identify this shape which has a hole in it, and is the inspiration for the common saying that topologists can't tell a co ee mug from a donut.
This shape can be described in Cartesian coordinates by the equation   2 2 2 2 2c− x +y +z = a .
torus [prompt on donut before read, accept ring torus before read, accept 1-torus]