job: 444_sigma_v58 (largest component of the solution)
X(G) recomputed from V,E equals the SAT cells: True
f-vector: (49, 87, 39, 0)  chi: 1  bounding box: [0, 0, 0] [3, 3, 3]
connected: True  complex: True
induced: False  non-edges: 12
corners (definition): []  corners (Lemma 2.1): []
#maximal cells per vertex: {2: 12, 3: 25, 4: 6, 5: 3, 6: 3}
Betti over GF(2): (1, 0, 0, 0)
Betti over GF(3): (1, 0, 0, 0)
Betti over GF(10007): (1, 0, 0, 0)
integer homology: [(1, []), (0, []), (0, []), (0, [])]
X(G) collapsible (greedy): True 87 collapses, restarts 0
  replayed: True [((3, 3, 1), ())]
all 21 pieces (3 directions, alpha in Z/2) collapsible: True
sigma-invariant: True
order of stabiliser in the 48 symmetries of [0,3]^3: 3
VERDICT: counterexample to Conjecture 1.1: True
edge list written (format [p, i] = edge p -- p+e_i)
edges: 002-003 002-012 002-102 003-013 003-103 012-013 012-112 013-023 013-113 020-021 020-030 020-120 021-022 021-031 021-121 022-032 022-122 023-033 023-123 030-031 030-130 031-032 032-033 032-132 033-133 102-103 102-112 102-202 103-203 112-113 112-122 112-212 113-123 120-121 120-130 121-122 121-131 121-221 122-123 122-132 122-222 123-133 130-131 130-230 131-231 132-133 200-201 200-210 200-300 201-211 201-301 202-203 202-212 203-213 203-303 210-211 210-220 210-310 211-212 211-221 211-311 212-213 212-222 212-312 213-313 220-221 220-320 221-222 221-231 221-321 230-231 230-330 231-331 300-301 300-310 301-302 301-311 302-303 302-312 303-313 310-320 311-312 312-313 320-321 320-330 321-331 330-331
