A two-circle roller is formed from two congruent circles of radius 
in perpendicular planes, joined
with their centers separated by 
(Stewart 1966). It can be made from two interlocking
thin disks. Choosing Cartesian
coordinates with the origin at the midpoint
of the centers and the 
-axis through them, the circles
satisfy
 |  |  |
(1)
|
 |  |  |
(2)
|
For uniform equal-mass disks, the center of mass lies at the midpoint of their centers. As the roller moves on a plane, its center of mass remains at the constant height (Stewart 1966)
 |
(3)
|
The oloid instead is the convex hull of two circles of radius 
whose centers are separated by 
.
