An n_k ctheorem (configurational theorem) is a set of n points and n hyperplanes with k points on each hyperplane and k hyperplanes through each point, all embedded in (k-1)-dimensional space.  (The type of space could be e.g. a projective (or affine) space over a general commutative field (type (0)), over a general possibly non-commutative field (type (1)), or over a general field of prime characteristic p (type (p)).  If the existence of n-1 hyperplanes implies the existence of the n'th hyperplane then it is called a "ctheorem".

Those known are:

Desargues 10_3 (type (1)) discovered about 1650 CE

Pappus 9_3 (type (0)) discovered about 300 CE

Moebius 8_4 (type (0)) discovered 1828 by A.F. Mobius

Glynn 8_4 (type (0)) discovered 2010 by  D.G. Glynn (Theorems of points and planes ...)

Glynn 9_4 (type (1)) discovered 2010 by D.G. Glynn (same paper)

Fano 7_3 (type (2)) known to geometers in the late19th century (the matroid dual is a 7_4 ctheorem of type (2) also)  Could be called "anti-Fano" since Fano's axiom proscribed it in the geometry.  It is also called PG(2,2), the projective geometry of dimension 2 over the finite field GF(2).

Note that the matroid dual of an n_k ctheorem is also a ctheorem n_{n-k} (if type (0) or (p)), so Pappus gives a ctheorem in 5-d space.  The two 8_4's (they are unique) are self-matroid-dual.  (Sometimes the matroid dual is a bit degenerate, as in the cases 10_3 and 9_4.)