A closed knight's tour of a chessboard uses legal moves of the knight to visit every square exactly once and return to its starting position. In 1991 Schwenk completely classified the m x n rectangular chessboards that admit a closed knight's tour. In honor of the upcoming twentieth anniversary of the publication of Schwenk's paper, this article extends his result by classifying the i x j x k rectangular prisms that admit a closed knight's tour.
The Electronic Journal of Combinatorics
DeMaio, J., & Mathew B. (2011). Which chessboards have a closed knight's tour within the rectangular prism? Electronic Journal of Combinatorics, 18(1), 1-8.