 TOPICS # Oloid Let two disks of radius intersect one another perpendicularly and have a diameter in common. If the distance between the centers of the disks is times their radius, then the distance from the center of gravity remains constant and so the object, known as a "two circle roller," rolls smoothly (Nishihara).  If the distance of two centers of disk is equal to the radius, then the convex hull produces another figure that rolls smoothly and is known as the oloid (Schatz 1975, p. 122; Nishihara), illustrated above. The oloid is an octic surface (Trott 2004, pp. 1194-1196).

For circles of radii , the surface area of the resulting oloid is (the same as that of a sphere with radius ), but no closed form is apparently known for the enclosed volume.

Octic Surface, Sphericon

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## References Capocasa, C. "Oloid." http://www.blackpoint.net/capocssa/oloid.htmlNishihara, A. "Oloid." http://www1.ttcn.ne.jp/~a-nishi/oloid/z_oloid.html.Nishihara, A. "Rolling Two Circle Roller." http://www1.ttcn.ne.jp/~a-nishi/oloid/z_ani_1.html.Schatz, P. "Das Oloid als Wälzkörper." §14 in Rythmusforschung und Technik. Stuttgart: Verlag Freies Geistesleben, 1975.Trott, M. The Mathematica GuideBook for Graphics. New York: Springer-Verlag, pp. 1194-1196, 2004. http://www.mathematicaguidebooks.org/.

## Cite this as:

Weisstein, Eric W. "Oloid." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Oloid.html