A query from a reader made me take a deep breath and finally admit that I’m a weird word as well as a person.
We are in the realm of bookbinding, specifically the folding and stitching of sheets of vellum, parchment or paper into a grouping called a quire. A set of four sheets was anciently standard, folded once to make eight leaves or sixteen pages. This was a quaternion. If instead you folded just one sheet of paper to make two leaves, it was called a bifolium; two sheets made four leaves and eight pages and was termed a binion; a ternion was created from three sheets. All these names came from Latin numbers.
You’re ahead of me, I expect. A quinion consisted of five sheets, folded and gathered. It’s from classical Latin quini, five each. Another word for it is quinternion and it’s possible that quinion, which is recorded only from late in the nineteenth century, is a truncated form of quinternion on the model of binion and ternion.
Early Irish manuscripts tend to be composed of quinions, quires of five sheets of parchment, laid one on top of another and folded. This made a gathering of ten leaves or twenty pages.
Early Christian Ireland, by T M Charles-Edwards, 2000.
Incidentally, the ancient standard of four sheets is the source of quire, which comes via Old French from the Latin for four. Later, the link to a specific number of leaves was lost and quire could be any number of sheets; later still it settled on 24 but is now 25, twenty of which make up a ream of 500 sheets.
[My family name actually has nothing to do with bookbinding, but derives from Spanish Quiñones, originally a word meaning a type of shared farming tenancy that comes from the Latin for five. The first member of the English family came over from the Dutch Republic, formerly the Spanish Netherlands, with William of Orange at the Glorious Revolution of 1688. The family has spread to the US, Canada, Australia and elsewhere.]