{"rank":3,"n":12,"seq":3,"label":"3.12.3","id":"r3_n12_0******************0***************************************************************0****************************************************************************************************************************************","beta_invariant":42,"birational_type":null,"birational_type_components":null,"birational_type_method":null,"char_poly_splits":false,"char_set":"[]","expected_dimension_over_Z":14,"free_realization_space":true,"girth":3,"good_basis":null,"good_basis_v2":"1,4,7","is_binary":false,"is_coloopless":true,"is_connected":true,"is_divisionally_free":false,"is_graphic":false,"is_identically_self_dual":false,"is_laminar":true,"is_loopless":true,"is_nested":false,"is_orientable":true,"is_paving":true,"is_quaternary":false,"is_realizable":false,"is_realizable_char0":false,"is_regular":false,"is_self_dual":false,"is_series_parallel":false,"is_simple":true,"is_simplicial_arrangement":false,"is_supersolvable":false,"is_ternary":false,"is_three_lines":false,"is_transversal":true,"is_uniform":null,"n_automorphisms":7776,"n_bases":217,"n_circuits":471,"n_components":null,"n_connected_components":1,"n_cyclic_flats":5,"n_flats":74,"n_loops":0,"principal_ideal":true,"rs_characteristic_dimension_unexpected":false,"rs_characteristic_dimension_varies":false,"rs_characteristic_dimensions":"[{\"p\":0,\"d\":13}]","rs_characteristic_dimensions_method":"audited_free_chart","rs_dim":-1,"rs_is_regular_scheme":null,"rs_is_smooth_over_QQ":true,"rs_is_smooth_over_ZZ":true,"rs_n_qbar_components":null,"rs_regularity_method":null,"rs_regularity_witness":null,"rs_scheme_simple_core_id":null,"rs_singular_fiber_characteristics":"{\"kind\":\"finite\",\"primes\":[]}","rs_singular_fiber_characteristics_method":"smooth_over_ZZ","rs_singular_fiber_primes":null,"rs_singular_fiber_primes_method":null,"rs_smoothness_method":"audited_free_chart","rs_smoothness_witness":null,"singular_primes":null,"smooth_char_0":null,"status":"computed_realization_space","tutte_polynomial":"x_0^3 + 9*x_0^2 + 3*x_0*x_1 + 42*x_0 + x_1^9 + 3*x_1^8 + 6*x_1^7 + 10*x_1^6 + 15*x_1^5 + 21*x_1^4 + 28*x_1^3 + 36*x_1^2 + 42*x_1","realization_space":{"vars":["x1","x2","x3","x4","x5","x6","x7","x8","x9","x10","x11","x12","x13"],"ideal":["0"],"inequations":["x10*x13 - x11*x12","x10*x13 - x10 - x11*x12 + x11 + x12 - x13","x3*x10 - x3*x11 - x3*x12 + x3*x13 - x10*x13 + x11*x12","x11 - x13","x1*x11 - x1*x13 - x4*x10 + x4*x12 + x10*x13 - x11*x12","x2*x11 - x2*x13 - x4*x10 + x4*x12 + x10*x13 - x11*x12","x10 - x12","x5*x10 - x5*x12 - x6*x11 + x6*x13 - x10*x13 + x11*x12","x6*x11 - x6*x13 - x7*x10 + x7*x12 + x10*x13 - x11*x12","x8*x11 - x8*x13 - x9*x10 + x9*x12 + x10*x13 - x11*x12","x8*x13 - x9*x12","x8*x13 - x8 - x9*x12 + x9 + x12 - x13","x3*x8 - x3*x9 - x3*x12 + x3*x13 - x8*x13 + x9*x12","x9 - x13","x1*x9 - x1*x13 - x4*x8 + x4*x12 + x8*x13 - x9*x12","x2*x9 - x2*x13 - x4*x8 + x4*x12 + x8*x13 - x9*x12","x8 - x12","x5*x8 - x5*x12 - x6*x9 + x6*x13 - x8*x13 + x9*x12","x6*x9 - x6*x13 - x7*x8 + x7*x12 + x8*x13 - x9*x12","x6*x13 - x7*x12","x6*x13 - x6 - x7*x12 + x7 + x12 - x13","x3*x6 - x3*x7 - x3*x12 + x3*x13 - x6*x13 + x7*x12","x7 - x13","x1*x7 - x1*x13 - x4*x6 + x4*x12 + x6*x13 - x7*x12","x2*x7 - x2*x13 - x4*x6 + x4*x12 + x6*x13 - x7*x12","x6 - x12","x5 - x7","x5*x12 - x6*x13","x5*x12 - x5 - x6*x13 + x6 - x12 + x13","x3*x5 - x3*x6 + x3*x12 - x3*x13 - x5*x12 + x6*x13","x5 - x13","x1*x5 - x1*x13 - x4*x6 + x4*x12 - x5*x12 + x6*x13","x2*x5 - x2*x13 - x4*x6 + x4*x12 - x5*x12 + x6*x13","x12","x12 - 1","x3 - x12","x1 - x12","x2 - x12","x2*x13 - x4*x12","x2*x13 - x2 - x4*x12 + x4 + x12 - x13","x2*x3 - x2*x13 - x3*x4 - x3*x12 + x3*x13 + x4*x12","x4 - x13","x1 - x2","x1*x13 - x4*x12","x1*x13 - x1 - x4*x12 + x4 + x12 - x13","x1*x3 - x1*x13 - x3*x4 - x3*x12 + x3*x13 + x4*x12","x13","x13 - 1","x3 - x13","x3","x12 - x13","x3 - 1","x8*x11 - x9*x10","x8*x11 - x8 - x9*x10 + x9 + x10 - x11","x3*x8 - x3*x9 - x3*x10 + x3*x11 - x8*x11 + x9*x10","x9 - x11","x1*x9 - x1*x11 - x4*x8 + x4*x10 + x8*x11 - x9*x10","x2*x9 - x2*x11 - x4*x8 + x4*x10 + x8*x11 - x9*x10","x8 - x10","x5*x8 - x5*x10 - x6*x9 + x6*x11 - x8*x11 + x9*x10","x6*x9 - x6*x11 - x7*x8 + x7*x10 + x8*x11 - x9*x10","x6*x11 - x7*x10","x6*x11 - x6 - x7*x10 + x7 + x10 - x11","x3*x6 - x3*x7 - x3*x10 + x3*x11 - x6*x11 + x7*x10","x7 - x11","x1*x7 - x1*x11 - x4*x6 + x4*x10 + x6*x11 - x7*x10","x2*x7 - x2*x11 - x4*x6 + x4*x10 + x6*x11 - x7*x10","x6 - x10","x5*x10 - x6*x11","x5*x10 - x5 - x6*x11 + x6 - x10 + x11","x3*x5 - x3*x6 + x3*x10 - x3*x11 - x5*x10 + x6*x11","x5 - x11","x1*x5 - x1*x11 - x4*x6 + x4*x10 - x5*x10 + x6*x11","x2*x5 - x2*x11 - x4*x6 + x4*x10 - x5*x10 + x6*x11","x10","x10 - 1","x3 - x10","x1 - x10","x2 - x10","x2*x11 - x4*x10","x2*x11 - x2 - x4*x10 + x4 + x10 - x11","x2*x3 - x2*x11 - x3*x4 - x3*x10 + x3*x11 + x4*x10","x4 - x11","x1*x11 - x4*x10","x1*x11 - x1 - x4*x10 + x4 + x10 - x11","x1*x3 - x1*x11 - x3*x4 - x3*x10 + x3*x11 + x4*x10","x11","x11 - 1","x3 - x11","x10 - x11","x6*x9 - x7*x8","x6*x9 - x6 - x7*x8 + x7 + x8 - x9","x3*x6 - x3*x7 - x3*x8 + x3*x9 - x6*x9 + x7*x8","x7 - x9","x1*x7 - x1*x9 - x4*x6 + x4*x8 + x6*x9 - x7*x8","x2*x7 - x2*x9 - x4*x6 + x4*x8 + x6*x9 - x7*x8","x6 - x8","x5*x8 - x6*x9","x5*x8 - x5 - x6*x9 + x6 - x8 + x9","x3*x5 - x3*x6 + x3*x8 - x3*x9 - x5*x8 + x6*x9","x5 - x9","x1*x5 - x1*x9 - x4*x6 + x4*x8 - x5*x8 + x6*x9","x2*x5 - x2*x9 - x4*x6 + x4*x8 - x5*x8 + x6*x9","x8","x8 - 1","x3 - x8","x1 - x8","x2 - x8","x2*x9 - x4*x8","x2*x9 - x2 - x4*x8 + x4 + x8 - x9","x2*x3 - x2*x9 - x3*x4 - x3*x8 + x3*x9 + x4*x8","x4 - x9","x1*x9 - x4*x8","x1*x9 - x1 - x4*x8 + x4 + x8 - x9","x1*x3 - x1*x9 - x3*x4 - x3*x8 + x3*x9 + x4*x8","x9","x9 - 1","x3 - x9","x8 - x9","x6","x6 - 1","x3 - x6","x1 - x6","x2 - x6","x2*x7 - x4*x6","x2*x7 - x2 - x4*x6 + x4 + x6 - x7","x2*x3 - x2*x7 - x3*x4 - x3*x6 + x3*x7 + x4*x6","x4 - x7","x1*x7 - x4*x6","x1*x7 - x1 - x4*x6 + x4 + x6 - x7","x1*x3 - x1*x7 - x3*x4 - x3*x6 + x3*x7 + x4*x6","x7","x7 - 1","x3 - x7","x6 - x7","x2*x5 - x4*x6","x2*x5 - x2 - x4*x6 + x4 - x5 + x6","x2*x3 - x2*x5 - x3*x4 + x3*x5 - x3*x6 + x4*x6","x4 - x5","x1*x5 - x4*x6","x1*x5 - x1 - x4*x6 + x4 - x5 + x6","x1*x3 - x1*x5 - x3*x4 + x3*x5 - x3*x6 + x4*x6","x5","x5 - 1","x3 - x5","x5 - x6","x2","x2 - 1","x2 - x3","x1","x1 - 1","x1 - x3","x4","x4 - 1","x3 - x4","x2 - x4","x1 - x4"],"matrix":[["1","1","1","0","1","1","0","1","1","1","1","1"],["0","1","x3","1","x1","x2","0","x6","x6","x8","x10","x12"],["0","1","x3","0","x4","x4","1","x5","x7","x9","x11","x13"]]}}