CoM | Twists and Turns: Enumerating the topological classes of knots/links on a 9x9x9 Rubik’s cube

Thursday, August 21, 2025
 – Live Presentation with
Tatyana Khodorovskiy and David Plaxco–

Session at 12 Noon Atlanta time
(check your time here)

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Twists and Turns: Enumerating the topological classes of knots/links on a 9x9x9 Rubik’s cube

In this talk, we will discuss joint work in which we have classified and enumerated the possible topological classes of “photogenic knots” that can be depicted on a 9-layered Rubik’s cube, with a certain edge permutation. In prior work, David lowered the enumeration to 128 distinct patterns using a group action, but Tanya has lowered this even further using Reidemeister moves and tangle moves to identify 54 distinct knots in this class of patterns.

Dr. Tatyana Khodorovskiy is a Doctoral Lecturer in the Mathematics and Statistics Department at Hunter College, CUNY. She earned her B.A. from NYU and her Ph.D. in Mathematics from Harvard University in 2012, where she specialized in low-dimensional topology. Originally from Kyiv, Ukraine, she moved to New York City in 1992 and now lives there with her family. At Hunter, she oversees multi-section courses in the sequence leading up to calculus, and designs curriculums using open educational resources. A couple of years ago she started creating patterns on large Rubik’s cubes and exploring their rich connection to mathematics.

Dr. David Plaxco is a Lecturer in the Department of Mathematics at the University of Georgia, specializing in undergraduate mathematics education and recreational mathematics. His work encompasses NSF-funded curriculum development and instructional videogame design, each focused on supporting student understanding in Linear Algebra. David has been creating Rubik’s Cube art since 2017 and sharing it within the broader mathematics community at JMM, G4G, Bridges, and other events.

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