Algebraic varieties named for this shape are subject to the orbit–cone correspondence (10[1])and can be constructed (10[2])from fans. For knots named for this shape, “x-to-the-p equals y-to-the-q” is a relation of the knot group. “R-squared” (10[1])quotient “Z-squared” is isomorphic to this (10[1])surface, (10[1])which has “Z-cross-Z” (10[1]-5[1])as its (10[1])fundamental group. (10[6])This (-5[2])surface can (10[1])be obtained (10[2])by gluing (-5[1])each pair of opposite (10[1]-5[2])edges (0[1]-5[9])of the (-5[1])unit (-5[1])square (10[1]-5[4])in the (10[1]-5[1])same (10[1])direction. (10[1]-5[5])This (10[1]-5[1])orientable (10[3])surface (10[2]-5[1])with Euler (-5[1])characteristic (-5[1])zero (-5[2])is the Cartesian product (-5[2])of two circles. (10[1]-5[2])Depending (10[1])on orientation, (10[1]-5[1])either a (-5[1])Klein bottle (-5[1])or this (-5[2])genus-one (-5[4])surface (10[1]-5[4])is formed (-5[2])by joining the circular (-5[2])ends of a cylinder. (10[2]-5[4])For 10 points, the surface of a coffee cup is topologically (10[2])equivalent (10[4]-5[1])to what single-holed (10[3]-5[1])surface (10[4])shaped like a (10[1])doughnut? (10[1])■END■ (10[43]0[6])