Wilson Stothers, Grassmann cubics and desmic structures,
Forum Geometricorum, 6 (2006) 117--138.

Abstract:  We show that each cubic of type nK which is not of type cK can be described as a Grassmann cubic. The geometry associates with each such cubic a cubic of type pK.  We call this the parent cubic. On the other hand, each cubic of type 
pK has infinitely many child cubics. The key is the existence of a desmic structure associated with parent and child. This extends work of Wolk by showing that, not only do (some) points of a desmic structure lie on a cubic, but also that they actually generate the cubic as a locus. Along the way, we meet many familiar cubics.

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