This broadly-accessible talk will introduce certain finite collections of vectors in $2n$-dimensional Euclidean space with combinatorial and geometrical properties that are useful in the study of quantum logic.
These configurations generalize the $4$-dimensional configurations employed by Peres (1993), Navara and Pt\'{a}k (2004), and others in various treatments of the Kochen-Specker theorem.
We will discuss applications, including the characterization of certain group-valued measures on the closed subspaces of Hilbert space, and we will conclude with several open problems.
This work is joint with John Harding and Ekaterina Jager.