job: 444_sigma_v61
X(G) recomputed from V,E equals the SAT cells: True
f-vector: (59, 108, 51, 1)  chi: 1  bounding box: [0, 0, 0] [3, 3, 3]
connected: True  complex: True
induced: False  non-edges: 21
corners (definition): []  corners (Lemma 2.1): []
#maximal cells per vertex: {2: 24, 3: 15, 4: 12, 5: 3, 6: 3, 7: 2}
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 109 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: 001-002 001-011 001-101 002-003 002-102 003-013 003-103 010-011 010-020 010-110 011-021 011-111 012-013 012-022 012-112 013-023 013-113 020-021 020-030 021-031 021-121 022-023 022-032 022-122 023-033 030-031 030-130 031-131 032-033 032-132 033-133 100-101 100-110 100-200 101-102 101-111 102-103 102-112 103-113 110-111 110-210 111-112 111-121 111-211 112-113 112-122 112-212 120-121 120-130 120-220 121-122 121-131 121-221 122-123 122-132 122-222 123-133 123-223 130-131 130-230 132-133 132-232 200-210 200-300 201-202 201-211 201-301 202-203 202-212 202-302 203-213 203-303 210-211 210-310 211-212 211-221 211-311 212-213 212-222 212-312 213-223 213-313 220-221 220-230 220-320 221-222 221-231 221-321 222-223 222-232 222-322 230-330 231-232 231-331 300-301 300-310 301-302 301-311 302-303 303-313 310-311 312-313 312-322 320-321 320-330 321-322 321-331 330-331
