PASS every half-edge lies in two corners
     cyclic order of half-edges at the vertex: a1^out b1^in a1^in b1^out a2^out b2^in a2^in b2^out
PASS link of the vertex is the single cycle a1o b1i a1i b1o a2o b2i a2i b2o
PASS a1, b1, c=a1a2, b2, a2 is a chain (crossings at the vertex: consecutive 1, others 0; c simple)
PASS A1 maps the relator to a conjugate of itself
PASS B1 maps the relator to a conjugate of itself
PASS C maps the relator to a conjugate of itself
PASS B2 maps the relator to a conjugate of itself
PASS A2 maps the relator to a conjugate of itself
PASS A1 acts on H_1 by a symplectic matrix
PASS B1 acts on H_1 by a symplectic matrix
PASS C acts on H_1 by a symplectic matrix
PASS B2 acts on H_1 by a symplectic matrix
PASS A2 acts on H_1 by a symplectic matrix
PASS image in GL(4,F_2) has order 720 = |Sp(4,2)| (found 720)
PASS image in GL(4,F_3) has order 51840 = |Sp(4,3)| (found 51840)
PASS Dehn algorithm sanity
PASS braid relation A1 B1^-1 A1 = B1^-1 A1 B1^-1 in Out(pi) (opposite handedness), conjugator ()
PASS braid relation B1 C^-1 B1 = C^-1 B1 C^-1 in Out(pi) (opposite handedness), conjugator ()
PASS braid relation C B2^-1 C = B2^-1 C B2^-1 in Out(pi) (opposite handedness), conjugator ()
PASS braid relation B2 A2^-1 B2 = A2^-1 B2 A2^-1 in Out(pi) (opposite handedness), conjugator ()
PASS A1 and C commute (already as automorphisms of the free group)
PASS A1 and B2 commute (already as automorphisms of the free group)
PASS A1 and A2 commute (already as automorphisms of the free group)
PASS B1 and B2 commute (already as automorphisms of the free group)
PASS B1 and A2 commute (already as automorphisms of the free group)
PASS C and A2 commute (already as automorphisms of the free group)
PASS polygon model: #components of preimage of S_2-(a1 u a2) = #orbits of <x,uxu^-1,v,wvw^-1> for 63678 homomorphisms (mismatches 0)
ALL CHECKS PASSED
