The Kinetic Alphabet, applied to fans
This page is short because the honest version is short. Fans are single-ended props, so they translate from staves the way clubs do: pretend one end of the staff got cut off and do everything else the same. A fan's orientation is the staff's thumb orientation, the flat face makes it easy to read at a glance, and every grid position, letter, and timing relationship applies unchanged. The full single-ended story lives on the club page, and all of it holds for fans.
What fans have that no tubular prop has is a plane. The leaves form a fan plane the way a triad's arms form a triangle plane, and the notation currently assumes the prop's plane matches the plane it's being spun on. Folds break that assumption. A fold doesn't travel through the grid's two-dimensional space at all: it leaves the plane, passes through 3D space, and lands back where it started with your hand orientation switched from front to back. Hand orientation isn't a concept in The Kinetic Alphabet yet. Mapping the full hand orientation matrix into pictographs is on the drawing board, not in the system, and folds are so fundamental to fans that this page has to say so plainly: until that piece lands, the notation captures less of fan spinning than fan spinners deserve.