This Gallery is a part of the project Space Curves Made from Circles, conducted by

Clark Kimberling
University of Evansville


Peter Moses
Moparmatic Co.
Redditch, Worcestershire, UK

The project includes a research article, to be published elsewhere.

Each curve has all these properties:

* occupies 3-dimensional space; will not fit in a plane
* made from circular arcs
* inscribed on a sphere
* inscribed in the faces of a regular polyhedron
* circumscribes various interesting objects
* closed
* smooth (in the calculus sense).

Each curve is polyhedral polyarc with polysyllabic name and nickname:

   Cubic Quadrarc: CQ
   Short Cubic Hexarc: SCH
   Long Cubic Hexarc: LCH
   Short Tetrahedral Quadrarc: STQ
   Long Tetrahedral Quadrarc: LTQ
   Short Octahedral Hexarc: SOH
   Long Octahedral Hexarc: LOH
   Short Dodecahedral Hexarc: SDH
   Long Dodecahedral Hexarc: LDH
   Short Dodecahedral Decarc: SDD
   Long Dodecahedral Decarc: LDD
   Short Icosahedral Decarc: SID
   Long Icosahedral Decarc: LID
   Hybrid Octahedral Octarc: SSLLSSLL
   Dodecahedral(1,1,1,1,3,3,1,1,1,1,3,3): D(111133111133)

To view a curve, click its name - and then use your browser's BACK to return to this page.
Curves 1-17 first appeared here on August 5, 2009.
Curves 18-22 first appeared on August 21, 2009.

1.     CQ on Sphere and Cylinders

2.     Animated Point on CQ

3.     Animated Sphericon with CQ

4.     Animated Conic Surface of CQ

5.     SCH in a Cube, with Inscribed Regular Hexagon

6.     LCH in a Cube, with Inscribed Cube Octahedron

7.     Animated LCH in a Cube, with Inscribed Cube Octahedron

8.     Animated Conic Surface of STQ

9.     LOH on Sphere and Octahedron (1st view, "the owl")

10.   LOH on Sphere and Octahedron (2nd view)

11.   LDD on Dodecahedron

12.   Animated Point on LDD

13.   Animated Point on LDD (opaque)

14.   Animated LID

15.   Animated LID on Truncated Icosahedron

16.   Animated SSLLSSLL

17.   Animated Point on SSLLSSLL

18.   Animated D(111133111133)

19.   Animated LOH on Sphere

20.   Animated SOH on Octahedron

21.   Animated LDH on Sphere

22.   Animated SDH on Dodecahedron