Which chessboards have a closed knight's tour within the rectangular prism? (Q625370)

Summary: 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 [\textit{A.J. Schwenk}, ``Which rectangular chessboards have a knight's tour?'' Math. Mag. 64, No.\,5, 325--332 (1991; Zbl 0761.05041)] completely classified the \(m \times n\) 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 \(i \times j \times k\) rectangular prisms that admit a closed knight's tour.