Permutations of the Octagon: An Aesthetic-Mathematical Dialectic

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James Mai: Permutations of the Octagon: An Aesthetic-Mathematical Dialectic. In: Bridges 2015. Pages 69–76



Artist James Mai employs permutational and combinatorial methods to produce sets of geometric forms for inclusion in his paintings and digital prints. Recent art works include form-sets comprised of form-variants derived from the regular octagon. The artist explains the process by which he creates the form-sets, the geometric features of the form-variants that constitute each form-set, and how the form-sets are composed in art works. In addition to first-order characteristics related to permutation rules, second-order characteristics of symmetry are found in the form-sets and are included in the art works. The permutational and symmetry characteristics of the form-sets are intended as the principal content of the art works and as such are designed to be visually comprehensible, apart from verbal or mathematical explanation. To that end, both mathematical and visual-aesthetic requirements influence the development of permutational form-sets from the start. This “aesthetic-mathematical dialectic” is critical to the development of art works whose mathematical content is adapted and responsive to visual perception.

Extended Abstract


 author      = {James Mai},
 title       = {Permutations of the Octagon: An Aesthetic-Mathematical Dialectic},
 pages       = {69--76},
 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] J. Mai and D. Zielinski, Permuting Heaven and Earth: Painted Expressions of Burnside’s Theorem, in Bridges Conference Proc. 2004, eds. R. Sarhangi and C. Séquin, pp. 95-102.

[2] S. Palmer, Vision Science: Photons to Phenomenology. Cambridge: The MIT Press, 1999.


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