Three Families of Mitered Borromean Ring Sculptures

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Tom Verhoeff and Koos Verhoeff: Three Families of Mitered Borromean Ring Sculptures. In: Bridges 2015. Pages 53–60



Artists have drawn inspiration from many mathematical structures, such as regular tilings, lattices, symmetry groups, regular polyhedra, knots, and links. A particularly well-known link goes by the name Borromean rings. It consists of three closed loops (“rings”) that cannot be taken apart without cutting, but after removing any one of the rings, the other two can be separated without cutting. In this paper, we present three families of sculptures involving miter joints, inspired by the Borromean rings.

Extended Abstract


 author      = {Tom Verhoeff and Koos Verhoeff},
 title       = {Three Families of Mitered Borromean Ring Sculptures},
 pages       = {53--60},
 booktitle   = {Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture},
 year        = {2015},
 editor      = {Kelly Delp, Craig S. Kaplan, Douglas McKenna and Reza Sarhangi},
 isbn        = {978-1-938664-15-1},
 issn        = {1099-6702},
 publisher   = {Tessellations Publishing},
 address     = {Phoenix, Arizona},
 note        = {Available online at \url{ }},
 url         = { },

Used References

[1] Jim Belk. Borromean Rings Illusion. Wikipedia. Borromean_Rings_Illusion.png (accessed 13 Jan. 2015)

[2] P. R. Cromwell, E. Beltrami, M. Rampichini. “The Borromean Rings”, Mathematical Intelligencer, 20(1):53–62 (1998). Extra material at

[3] Bruno Ernst, Rinus Roelofs (Eds.). Koos Verhoeff. Foundation Ars et Mathesis, 2013. http://www.

[4] C. Gunn, J. M. Sullivan. “The Borromean Rings: A Video about the New IMU Logo”, Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture, pp. 63–70, 2008.

[5] Alan Holden. Orderly Tangles: Cloverleafs, Gordian Knots, and Regular Polylinks. Columbia University Press, 1983.

[6] Slavik V. Jablan. “Are Borromean Links So Rare?”, Forma 14(4):269–277 (1999).

[7] B. Lindstr¨om, H.-O. Zetterstr¨om. “Borromean circles are impossible”, Amer. Math. Monthly, 98(4):340–341 (1991).

[8] John Robinson. Symbolic Sculpture.

[9] Carlo H. S´equin. “Splitting Tori, Knots, and Moebius Bands”, Renaissance Banff: Mathematics, Music, Art, Culture. pp. 211–218, 2005.

[10] Tom Verhoeff, Koos Verhoeff. “The Mathematics of Mitering and Its Artful Application”, Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture, pp. 225–234, 2008.

[11] Tom Verhoeff. “3D Turtle Geometry: Artwork, Theory, Program Equivalence and Symmetry”. Int. J. of Arts and Technology, 3(2/3):288–319 (2010).

[12] Tom Verhoeff, Koos Verhoeff. “From Chain-link Fence to Space-spanning Mathematial Structures”, Proceedings of Bridges 2011: Mathematics, Music, Art, Architecture, Culture, pp. 73–80, 2011.


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