@Seedfork A quick search of the thesis produced as a first "hit" this,
"After their production cycle in the field, their foliage is cut off and they are machine harvested, with the majority of their roots also removed. Each plant is then split up by dividing its crown into smaller plants called eyes, or clumps of the rhizomes; each eye can be sold as a new daylily plant."
Then this,
"Daylily plants are grown in the field for up to 3 years and then are commercially propagated by dividing the crown, which consists of many individual plants called eyes"
I interpret "eyes" to mean the number of fans.
