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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