Artwork Inspired by Dual Dodecahedra and Icosahedra

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Stephen Wassell and Mark Reynolds: Artwork Inspired by Dual Dodecahedra and Icosahedra. In: Bridges 2017, Pages 125–130.



A long-standing collaboration between an artist and a mathematician bears new fruit in the form of novel geometric constructions and several works of art based on them. The inspiration for the present collaboration is a recent result on the edge-length ratios between dual regular dodecahedra and icosahedra, specifically the two vertex-to-face pairings of these dual Platonic solids: when the icosahedron circumscribes the dodecahedron, the edge-length ratio is 𝜙/3, and conversely, when the dodecahedron circumscribes the icosahedron, the edge-length ratio is 𝜙2/√5, where 𝜙 is the golden number. These two edge-length ratios are the basis for the geometric constructions and the resulting artwork, which highlight interesting characteristics of the two ratios, both individually and as they relate to each other.

Extended Abstract


 author      = {Stephen Wassell and Mark Reynolds},
 title       = {Artwork Inspired by Dual Dodecahedra and Icosahedra},
 pages       = {125--130},
 booktitle   = {Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture},
 year        = {2017},
 editor      = {David Swart, Carlo H. S\'equin, and Krist\'of Fenyvesi},
 isbn        = {978-1-938664-22-9},
 issn        = {1099-6702},
 publisher   = {Tessellations Publishing},
 address     = {Phoenix, Arizona},
 note        = {Available online at \url{}}

Used References

[1] “MARK REYNOLDS: June 12 2015 – July 12 2015” (appeared in The New Yorker, July 6 & 13, 2015, p. 16). Retrieved from (as of January 17, 2017).

[2] Branko Mitrović and Stephen R. Wassell, eds. Andrea Palladio: Villa Cornaro in Piombino Dese. New York: Acanthus Press. 2006.

[3] Mark A. Reynolds. “Geometric and Harmonic Means and Progressions,” Nexus Network Journal, 3, n. 2, pp. 147–150. 2001.

[4] Stephen R. Wassell. “Arithmetic, Geometric and Harmonic Sequences,” Nexus Network Journal, 3, n. 2, pp. 151–155. 2001.

[5] Stephen R. Wassell and Samantha Benito. “Edge-length ratios between dual Platonic solids: a surprisingly new result involving the golden ratio,” The Fibonacci Quarterly, 50, n. 2, pp. 144–154. 2012.

[6] Kim Williams, Lionel March, and Stephen R. Wassell, eds. The Mathematical Works of Leon Battista Alberti. Boston: Birkhäuser Verlag. 2010.


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