// readme

W(3,3)

One finite geometry, pushed as far as exact computation goes

40 points Ā· 40 lines Ā· SRG(40,12,2,4) Ā· Aut ≅ W(E₆), order 51,840

Thousands of exact artifacts. Named maps, not matching integers. Reproducible certificates. Public corrections.

Read the atlas Ā· Master paper Ā· W33 for Everyone Ā· Find a result Ā· What we got wrong


Start with the symplectic space Fā‚ƒā“. Its totally isotropic points and lines form the generalized quadrangle W(3,3): 40 points, 40 lines, each point on 4 lines, and a collinearity graph SRG(40,12,2,4) whose automorphism group is PGSp(4,3) ≅ W(E₆). It is also the commutation geometry of two qutrits: the 40 points are the two-qutrit Pauli operators up to phase and powers, two points are collinear when the operators commute, and the 40 lines are the maximal commuting sets.

This repository is everything that has been computed exactly from that one object:…