A common parameterization of Boy's surface in was by given by Apery in 1986 as:
,
,
,
where , , and . As the parameter goes to zero, Boy's surface smoothly transforms into the Roman surface. Values in between 0 and 1 are interpreted as a mixture of the Roman surface and Boy's surface, which are topologically equivalent. Both surfaces can be obtained by attaching a Möbius strip to the circumference of a circle and stretching it until it forms a closed surface.