Photogenic Knot Projections on n×n×n Rubik’s Cubes
David Plaxco

Proceedings of Bridges 2022: Mathematics, Art, Music, Architecture, Culture
Pages 331–334
Short Papers

Abstract

In this paper, I outline one set of criteria for categorizing pixelated projections of knots and use these criteria to define photogenic knot projections. I then explain how these photogenic projections can be created on the n×n×n Rubik’s cube and identify three aspects of photogenic projections of knots – number of colors (c), number of faces used (f), and number of layers on the cube (l) – which can be used to characterize a projection. Finally, I define c,f,lphotogenic knot projections and discuss minimizations of some knots over c, f, and l.

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