{"schema":1,"title":"Nine-cube cross: one lattice corona, no second corona","date":"2026-09-24","scope":"Integer translations and proper cubic rotations; complete face, edge and vertex surrounds; no topological-ball requirement.","heesch":1,"sourceIndex":25373,"sourceCommit":"81eea57137d46dffb8fdc8c74e3c500845d3276b","root":[[-2,0,0],[-1,0,0],[0,-2,0],[0,-1,0],[0,0,0],[0,1,0],[0,2,0],[1,0,0],[2,0,0]],"corona":[[[-7,0,0],[-6,0,0],[-5,-2,0],[-5,-1,0],[-5,0,0],[-5,1,0],[-5,2,0],[-4,0,0],[-3,0,0]],[[-7,0,1],[-6,0,1],[-5,-2,1],[-5,-1,1],[-5,0,1],[-5,1,1],[-5,2,1],[-4,0,1],[-3,0,1]],[[-5,-3,-1],[-4,-3,-1],[-3,-3,-3],[-3,-3,-2],[-3,-3,-1],[-3,-3,0],[-3,-3,1],[-2,-3,-1],[-1,-3,-1]],[[-5,-2,-1],[-4,-2,-1],[-3,-2,-3],[-3,-2,-2],[-3,-2,-1],[-3,-2,0],[-3,-2,1],[-2,-2,-1],[-1,-2,-1]],[[-5,-1,2],[-4,-1,2],[-3,-1,0],[-3,-1,1],[-3,-1,2],[-3,-1,3],[-3,-1,4],[-2,-1,2],[-1,-1,2]],[[-3,-1,-1],[-3,0,-1],[-3,1,-3],[-3,1,-2],[-3,1,-1],[-3,1,0],[-3,1,1],[-3,2,-1],[-3,3,-1]],[[-3,2,-2],[-2,2,-2],[-1,2,-4],[-1,2,-3],[-1,2,-2],[-1,2,-1],[-1,2,0],[0,2,-2],[1,2,-2]],[[-3,3,-2],[-2,3,-2],[-1,3,-4],[-1,3,-3],[-1,3,-2],[-1,3,-1],[-1,3,0],[0,3,-2],[1,3,-2]],[[-2,-3,-2],[-2,-2,-2],[-2,-1,-4],[-2,-1,-3],[-2,-1,-2],[-2,-1,-1],[-2,-1,0],[-2,0,-2],[-2,1,-2]],[[-2,-3,1],[-1,-3,1],[0,-5,1],[0,-4,1],[0,-3,1],[0,-2,1],[0,-1,1],[1,-3,1],[2,-3,1]],[[-2,-1,1],[-2,0,1],[-2,1,-1],[-2,1,0],[-2,1,1],[-2,1,2],[-2,1,3],[-2,2,1],[-2,3,1]],[[-2,0,-1],[-1,0,-1],[0,-2,-1],[0,-1,-1],[0,0,-1],[0,1,-1],[0,2,-1],[1,0,-1],[2,0,-1]],[[-1,-6,0],[-1,-5,0],[-1,-4,-2],[-1,-4,-1],[-1,-4,0],[-1,-4,1],[-1,-4,2],[-1,-3,0],[-1,-2,0]],[[-1,-5,-1],[0,-5,-1],[1,-7,-1],[1,-6,-1],[1,-5,-1],[1,-4,-1],[1,-3,-1],[2,-5,-1],[3,-5,-1]],[[-1,-4,3],[-1,-3,3],[-1,-2,1],[-1,-2,2],[-1,-2,3],[-1,-2,4],[-1,-2,5],[-1,-1,3],[-1,0,3]],[[-1,-3,-2],[-1,-2,-2],[-1,-1,-4],[-1,-1,-3],[-1,-1,-2],[-1,-1,-1],[-1,-1,0],[-1,0,-2],[-1,1,-2]],[[-1,-1,1],[-1,0,1],[-1,1,-1],[-1,1,0],[-1,1,1],[-1,1,2],[-1,1,3],[-1,2,1],[-1,3,1]],[[-1,5,-1],[0,5,-1],[1,3,-1],[1,4,-1],[1,5,-1],[1,6,-1],[1,7,-1],[2,5,-1],[3,5,-1]],[[-1,5,0],[0,5,0],[1,3,0],[1,4,0],[1,5,0],[1,6,0],[1,7,0],[2,5,0],[3,5,0]],[[0,-5,-3],[0,-4,-3],[0,-3,-5],[0,-3,-4],[0,-3,-3],[0,-3,-2],[0,-3,-1],[0,-2,-3],[0,-1,-3]],[[0,-3,0],[1,-3,0],[2,-5,0],[2,-4,0],[2,-3,0],[2,-2,0],[2,-1,0],[3,-3,0],[4,-3,0]],[[0,-2,3],[0,-1,3],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,0,5],[0,1,3],[0,2,3]],[[0,1,1],[0,2,1],[0,3,-1],[0,3,0],[0,3,1],[0,3,2],[0,3,3],[0,4,1],[0,5,1]],[[1,-4,-2],[1,-3,-2],[1,-2,-4],[1,-2,-3],[1,-2,-2],[1,-2,-1],[1,-2,0],[1,-1,-2],[1,0,-2]],[[1,-3,2],[1,-2,2],[1,-1,0],[1,-1,1],[1,-1,2],[1,-1,3],[1,-1,4],[1,0,2],[1,1,2]],[[1,-2,1],[2,-2,1],[3,-4,1],[3,-3,1],[3,-2,1],[3,-1,1],[3,0,1],[4,-2,1],[5,-2,1]],[[1,-1,-3],[1,0,-3],[1,1,-5],[1,1,-4],[1,1,-3],[1,1,-2],[1,1,-1],[1,2,-3],[1,3,-3]],[[1,-1,-1],[2,-1,-1],[3,-3,-1],[3,-2,-1],[3,-1,-1],[3,0,-1],[3,1,-1],[4,-1,-1],[5,-1,-1]],[[1,0,1],[1,1,1],[1,2,-1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,1],[1,4,1]],[[1,1,0],[2,1,0],[3,-1,0],[3,0,0],[3,1,0],[3,2,0],[3,3,0],[4,1,0],[5,1,0]],[[2,-3,3],[2,-2,3],[2,-1,1],[2,-1,2],[2,-1,3],[2,-1,4],[2,-1,5],[2,0,3],[2,1,3]],[[2,-1,-3],[2,0,-3],[2,1,-5],[2,1,-4],[2,1,-3],[2,1,-2],[2,1,-1],[2,2,-3],[2,3,-3]],[[2,0,1],[2,1,1],[2,2,-1],[2,2,0],[2,2,1],[2,2,2],[2,2,3],[2,3,1],[2,4,1]],[[3,-1,3],[3,0,3],[3,1,1],[3,1,2],[3,1,3],[3,1,4],[3,1,5],[3,2,3],[3,3,3]]],"verification":{"formula":{"variables":8140,"first_candidates":686,"root_required_cells":90,"overlap_pairs":509064,"clauses":569020},"geometry":{"one_corona_copies":34,"required_voxels":90,"distinct_orientations":3,"catalogue_identity":true,"independent_bounding_box_enumeration":true},"cnf_sha256":"102e050db3761b588d87e866168917802f9ad23e53fa40bf7000a476bd469b1d","drat_verified":true,"lrat_verified":true,"complete":true,"lrat_checker":"cake_lpr","drup_sha256":"e4249548054a3c78def6670b5bbbf34fc2e8cf5be4d857bcddb25030df91be34","lrat_sha256":"410db50eb118147dc82838a31903d6465e050a159cc2d895ed6ee9ec1c903326","elapsed_seconds":121.963},"package":{"file":"certificate-v1.tar.gz","bytes":53096088,"sha256":"c1d36e7bad4d2f20194e83c6eb61c061ad81c0f0a009ee9ab7b26cf90b865fa4","sourceCommit":"4deaff208effaa0408481d6635bc6e40cb7be9be","command":"python3 verify.py","requirements":"Python 3.9+, C99 compiler, x86-64 or ARM64, about 3 GB free disk and several GB available RAM","network":"None after downloading the archive"}}