The sheet number of a $2$-knot is a quantity which reflects the complexity of the knotting in $4$-space. The aim of this note is to determine the sheet numbers of the $2$- and $3$-twist-spun trefoils. For this purpose, we give a lower bound of the sheet number by the quandle cocycle invariant of a $2$-knot, and an upper bound by the crossing number of a $1$-knot.
Shin Satoh. "A note on the sheet numbers of twist-spun knots." Hiroshima Math. J. 40 (1) 1 - 15, March 2010. https://doi.org/10.32917/hmj/1270645079