"The hyperboloid of revolution (generated as a surface of revolution) is a special case of the elliptical hyperboloid... The shape of a small portion of the hyperboloid of revolution around the equator is similar to that of the , but larger portions are quite different, as are the s. The image of the Gauss map of the whole hyperboloid of revolution omits disks around the north and south poles, whereas the image of the Gauss map of the whole catenoid omits only the north and south poles."