Cube number can detect chirality and legendrian type of knots
For a knot K the cube number is a knot invariant defined to be the smallest n for which there is a cube diagram of size n for K. Examples of knots for which the cube number detects chirality are presented. An example is also presented of two Legendrian knots that, while topologically isotopic, are distinguished as Legendrian knots by cube number. © 2012 World Scientific Publishing Company.
Journal of Knot Theory and its Ramifications
McCarty, B. (2012). Cube number can detect chirality and legendrian type of knots. Journal of Knot Theory and its Ramifications, 21 (3) https://doi.org/10.1142/S0218216511009662