Reading graph: Number of vertices: 10 Dimension: ? Vertices: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Field generated by the entries of the Gram matrix: Q[sqrt(2)] File read Image created: testgraph.jpg Finding connected subgraphs...... Finding graphs products...... Connected spherical graphs Graphs of rank 0 Graphs of rank 1 A1 ; 1 A1 ; 2 A1 ; 3 A1 ; 4 A1 ; 5 A1 ; 6 A1 ; 7 A1 ; 8 A1 ; 9 A1 ; 10 Graphs of rank 2 A2 ; 1 2 A2 ; 2 3 A2 ; 3 4 A2 ; 3 10 A2 ; 4 5 A2 ; 5 6 A2 ; 6 7 A2 ; 7 8 G2 ; 8 9 (4) Graphs of rank 3 A3 ; 1 2 3 A3 ; 2 3 4 A3 ; 2 3 10 A3 ; 3 4 5 A3 ; 4 3 10 A3 ; 4 5 6 A3 ; 5 6 7 A3 ; 6 7 8 B3 ; 7 8 9 Graphs of rank 4 A4 ; 1 2 3 4 A4 ; 1 2 3 10 A4 ; 2 3 4 5 A4 ; 3 4 5 6 A4 ; 4 5 6 7 A4 ; 5 4 3 10 A4 ; 5 6 7 8 B4 ; 6 7 8 9 D4 ; 2 3 4 | 10 Graphs of rank 5 A5 ; 1 2 3 4 5 A5 ; 2 3 4 5 6 A5 ; 3 4 5 6 7 A5 ; 4 5 6 7 8 A5 ; 6 5 4 3 10 B5 ; 5 6 7 8 9 D5 ; 1 2 3 4 | 10 D5 ; 5 4 3 2 | 10 Graphs of rank 6 A6 ; 1 2 3 4 5 6 A6 ; 2 3 4 5 6 7 A6 ; 3 4 5 6 7 8 A6 ; 7 6 5 4 3 10 B6 ; 4 5 6 7 8 9 D6 ; 6 5 4 3 2 | 10 E6 ; 1 2 3 4 5 | 10 Graphs of rank 7 A7 ; 1 2 3 4 5 6 7 A7 ; 2 3 4 5 6 7 8 A7 ; 8 7 6 5 4 3 10 B7 ; 3 4 5 6 7 8 9 D7 ; 7 6 5 4 3 2 | 10 E7 ; 1 2 3 4 5 6 | 10 Graphs of rank 8 A8 ; 1 2 3 4 5 6 7 8 B8 ; 2 3 4 5 6 7 8 9 B8 ; 10 3 4 5 6 7 8 9 D8 ; 8 7 6 5 4 3 2 | 10 E8 ; 1 2 3 4 5 6 7 | 10 Graphs of rank 9 B9 ; 1 2 3 4 5 6 7 8 9 Graphs of rank 10 Connected euclidean graphs Graphs of rank 0 Graphs of rank 1 Graphs of rank 2 Graphs of rank 3 Graphs of rank 4 Graphs of rank 5 Graphs of rank 6 Graphs of rank 7 Graphs of rank 8 Graphs of rank 9 TB8 ; 9 | 8 7 6 5 4 3 2 | 10 TE8 ; 1 2 3 4 5 6 7 8 | 10 Graphs of rank 10 Product of euclidean graphs TE_8^1 | N: 1 TB_8^1 | N: 1 Computations...... Products of spherical graphs 1: A_1^1 | N: 10 / Order: 2 2: G_4^1 | N: 1 / Order: 8 2: A_2^1 | N: 8 / Order: 6 2: A_1^2 | N: 36 / Order: 4 3: B_3^1 | N: 1 / Order: 48 3: A_3^1 | N: 8 / Order: 24 3: A_1^1 | G_4^1 | N: 7 / Order: 16 3: A_1^1 | A_2^1 | N: 47 / Order: 12 3: A_1^3 | N: 57 / Order: 8 4: D_4^1 | N: 1 / Order: 192 4: B_4^1 | N: 1 / Order: 384 4: A_4^1 | N: 7 / Order: 120 4: A_2^1 | G_4^1 | N: 6 / Order: 48 4: A_2^2 | N: 13 / Order: 36 4: A_1^1 | B_3^1 | N: 6 / Order: 96 4: A_1^1 | A_3^1 | N: 38 / Order: 48 4: A_1^2 | G_4^1 | N: 15 / Order: 32 4: A_1^2 | A_2^1 | N: 84 / Order: 24 4: A_1^4 | N: 39 / Order: 16 5: D_5^1 | N: 2 / Order: 1920 5: B_5^1 | N: 1 / Order: 3840 5: A_5^1 | N: 5 / Order: 720 5: A_3^1 | G_4^1 | N: 6 / Order: 192 5: A_2^1 | B_3^1 | N: 5 / Order: 288 5: A_2^1 | A_3^1 | N: 19 / Order: 144 5: A_1^1 | D_4^1 | N: 4 / Order: 384 5: A_1^1 | B_4^1 | N: 5 / Order: 768 5: A_1^1 | A_4^1 | N: 27 / Order: 240 5: A_1^1 | A_2^1 | G_4^1 | N: 18 / Order: 96 5: A_1^1 | A_2^2 | N: 30 / Order: 72 5: A_1^2 | B_3^1 | N: 10 / Order: 192 5: A_1^2 | A_3^1 | N: 47 / Order: 96 5: A_1^3 | G_4^1 | N: 11 / Order: 64 5: A_1^3 | A_2^1 | N: 53 / Order: 48 5: A_1^5 | N: 9 / Order: 32 6: E_6^1 | N: 1 / Order: 51840 6: D_6^1 | N: 1 / Order: 23040 6: D_4^1 | G_4^1 | N: 1 / Order: 1536 6: B_6^1 | N: 1 / Order: 46080 6: A_6^1 | N: 4 / Order: 5040 6: A_4^1 | G_4^1 | N: 5 / Order: 960 6: A_3^1 | B_3^1 | N: 5 / Order: 1152 6: A_3^2 | N: 6 / Order: 576 6: A_2^1 | D_4^1 | N: 2 / Order: 1152 6: A_2^1 | B_4^1 | N: 4 / Order: 2304 6: A_2^1 | A_4^1 | N: 11 / Order: 720 6: A_2^2 | G_4^1 | N: 4 / Order: 288 6: A_2^3 | N: 1 / Order: 216 6: A_1^1 | D_5^1 | N: 7 / Order: 3840 6: A_1^1 | B_5^1 | N: 4 / Order: 7680 6: A_1^1 | A_5^1 | N: 13 / Order: 1440 6: A_1^1 | A_3^1 | G_4^1 | N: 11 / Order: 384 6: A_1^1 | A_2^1 | B_3^1 | N: 10 / Order: 576 6: A_1^1 | A_2^1 | A_3^1 | N: 25 / Order: 288 6: A_1^2 | D_4^1 | N: 3 / Order: 768 6: A_1^2 | B_4^1 | N: 6 / Order: 1536 6: A_1^2 | A_4^1 | N: 24 / Order: 480 6: A_1^2 | A_2^1 | G_4^1 | N: 12 / Order: 192 6: A_1^2 | A_2^2 | N: 18 / Order: 144 6: A_1^3 | B_3^1 | N: 5 / Order: 384 6: A_1^3 | A_3^1 | N: 15 / Order: 192 6: A_1^4 | G_4^1 | N: 2 / Order: 128 6: A_1^4 | A_2^1 | N: 9 / Order: 96 7: E_7^1 | N: 1 / Order: 2903040 7: D_7^1 | N: 1 / Order: 322560 7: D_5^1 | G_4^1 | N: 2 / Order: 15360 7: B_7^1 | N: 1 / Order: 645120 7: B_3^1 | D_4^1 | N: 1 / Order: 9216 7: A_7^1 | N: 3 / Order: 40320 7: A_5^1 | G_4^1 | N: 3 / Order: 5760 7: A_4^1 | B_3^1 | N: 4 / Order: 5760 7: A_3^1 | D_4^1 | N: 1 / Order: 4608 7: A_3^1 | B_4^1 | N: 4 / Order: 9216 7: A_3^1 | A_4^1 | N: 5 / Order: 2880 7: A_2^1 | D_5^1 | N: 3 / Order: 11520 7: A_2^1 | B_5^1 | N: 3 / Order: 23040 7: A_2^1 | A_5^1 | N: 2 / Order: 4320 7: A_2^1 | A_3^1 | G_4^1 | N: 3 / Order: 1152 7: A_2^2 | B_3^1 | N: 1 / Order: 1728 7: A_1^1 | E_6^1 | N: 3 / Order: 103680 7: A_1^1 | D_6^1 | N: 2 / Order: 46080 7: A_1^1 | D_4^1 | G_4^1 | N: 1 / Order: 3072 7: A_1^1 | B_6^1 | N: 3 / Order: 92160 7: A_1^1 | A_6^1 | N: 6 / Order: 10080 7: A_1^1 | A_4^1 | G_4^1 | N: 5 / Order: 1920 7: A_1^1 | A_3^1 | B_3^1 | N: 4 / Order: 2304 7: A_1^1 | A_3^2 | N: 3 / Order: 1152 7: A_1^1 | A_2^1 | D_4^1 | N: 1 / Order: 2304 7: A_1^1 | A_2^1 | B_4^1 | N: 4 / Order: 4608 7: A_1^1 | A_2^1 | A_4^1 | N: 10 / Order: 1440 7: A_1^1 | A_2^2 | G_4^1 | N: 3 / Order: 576 7: A_1^1 | A_2^3 | N: 1 / Order: 432 7: A_1^2 | D_5^1 | N: 4 / Order: 7680 7: A_1^2 | B_5^1 | N: 3 / Order: 15360 7: A_1^2 | A_5^1 | N: 6 / Order: 2880 7: A_1^2 | A_3^1 | G_4^1 | N: 3 / Order: 768 7: A_1^2 | A_2^1 | B_3^1 | N: 5 / Order: 1152 7: A_1^2 | A_2^1 | A_3^1 | N: 6 / Order: 576 7: A_1^3 | B_4^1 | N: 2 / Order: 3072 7: A_1^3 | A_4^1 | N: 4 / Order: 960 7: A_1^3 | A_2^1 | G_4^1 | N: 1 / Order: 384 7: A_1^3 | A_2^2 | N: 2 / Order: 288 8: E_8^1 | N: 1 / Order: 696729600 8: E_6^1 | G_4^1 | N: 1 / Order: 414720 8: D_8^1 | N: 1 / Order: 5160960 8: D_6^1 | G_4^1 | N: 1 / Order: 184320 8: B_8^1 | N: 2 / Order: 10321920 8: B_4^1 | D_4^1 | N: 1 / Order: 73728 8: B_3^1 | D_5^1 | N: 2 / Order: 92160 8: A_8^1 | N: 1 / Order: 362880 8: A_6^1 | G_4^1 | N: 1 / Order: 40320 8: A_5^1 | B_3^1 | N: 1 / Order: 34560 8: A_4^1 | B_4^1 | N: 2 / Order: 46080 8: A_4^2 | N: 1 / Order: 14400 8: A_3^1 | D_5^1 | N: 1 / Order: 46080 8: A_3^1 | B_5^1 | N: 2 / Order: 92160 8: A_2^1 | E_6^1 | N: 1 / Order: 311040 8: A_2^1 | B_6^1 | N: 1 / Order: 276480 8: A_2^1 | A_4^1 | G_4^1 | N: 1 / Order: 5760 8: A_1^1 | E_7^1 | N: 2 / Order: 5806080 8: A_1^1 | D_7^1 | N: 1 / Order: 645120 8: A_1^1 | D_5^1 | G_4^1 | N: 1 / Order: 30720 8: A_1^1 | B_7^1 | N: 1 / Order: 1290240 8: A_1^1 | A_7^1 | N: 2 / Order: 80640 8: A_1^1 | A_5^1 | G_4^1 | N: 1 / Order: 11520 8: A_1^1 | A_4^1 | B_3^1 | N: 2 / Order: 11520 8: A_1^1 | A_3^1 | B_4^1 | N: 1 / Order: 18432 8: A_1^1 | A_3^1 | A_4^1 | N: 1 / Order: 5760 8: A_1^1 | A_2^1 | D_5^1 | N: 1 / Order: 23040 8: A_1^1 | A_2^1 | B_5^1 | N: 2 / Order: 46080 8: A_1^1 | A_2^1 | A_5^1 | N: 1 / Order: 8640 8: A_1^1 | A_2^1 | A_3^1 | G_4^1 | N: 1 / Order: 2304 8: A_1^1 | A_2^2 | B_3^1 | N: 1 / Order: 3456 8: A_1^2 | E_6^1 | N: 1 / Order: 207360 8: A_1^2 | B_6^1 | N: 2 / Order: 184320 8: A_1^2 | A_6^1 | N: 1 / Order: 20160 8: A_1^2 | A_2^1 | B_4^1 | N: 1 / Order: 9216 8: A_1^2 | A_2^1 | A_4^1 | N: 1 / Order: 2880 9: E_7^1 | G_4^1 | N: 1 / Order: 23224320 9: B_9^1 | N: 1 / Order: 185794560 9: B_4^1 | D_5^1 | N: 1 / Order: 737280 9: B_3^1 | E_6^1 | N: 1 / Order: 2488320 9: A_4^1 | B_5^1 | N: 1 / Order: 460800 9: A_1^1 | E_8^1 | N: 1 / Order: 1393459200 9: A_1^1 | B_8^1 | N: 1 / Order: 20643840 9: A_1^1 | A_2^1 | B_6^1 | N: 1 / Order: 552960 ---------------------------------------------------------- Compactness test Trying to extend the product: A1 ; 1 A7 ; 8 7 6 5 4 3 10 Succeeded in 1 ways instead of 2 Candidate: A1 ; 1 B8 ; 10 3 4 5 6 7 8 9 ---------------------------------------------------------- Computation time: 2.67714s Information Guessed dimension: 9 Cocompact: no Finite covolume: yes f-vector: (10, 45, 120, 210, 252, 210, 120, 45, 10, 1) Number of vertices at infinity: 2 Alternating sum of the components of the f-vector: 2 Euler characteristic: 0 Signature (numerically): 9,1,0 Growth series: f(x) = C(2,2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,5,5,6,6,6,6,7,8,8,9,10,10,12,12,14,15,16,18,20,24,30)/(1 - x - x^2 + x^4 - x^7 + 2 * x^8 - x^9 - x^11 + 2 * x^12 - x^13 + x^14 - 2 * x^15 + 4 * x^16 - 2 * x^17 + 2 * x^18 - 4 * x^19 + 4 * x^20 - 3 * x^21 + 3 * x^22 - 5 * x^23 + 7 * x^24 - 6 * x^25 + 4 * x^26 - 8 * x^27 + 8 * x^28 - 7 * x^29 + 6 * x^30 - 11 * x^31 + 11 * x^32 - 9 * x^33 + 7 * x^34 - 13 * x^35 + 14 * x^36 - 12 * x^37 + 9 * x^38 - 14 * x^39 + 17 * x^40 - 12 * x^41 + 11 * x^42 - 17 * x^43 + 18 * x^44 - 11 * x^45 + 12 * x^46 - 17 * x^47 + 22 * x^48 - 12 * x^49 + 12 * x^50 - 15 * x^51 + 18 * x^52 - 10 * x^53 + 13 * x^54 - 15 * x^55 + 18 * x^56 - 7 * x^57 + 9 * x^58 - 13 * x^59 + 15 * x^60 - 5 * x^61 + 4 * x^62 - 9 * x^63 + 11 * x^64 - 2 * x^65 + x^66 - 8 * x^67 + 5 * x^68 + 3 * x^69 - 5 * x^70 - 5 * x^71 + 2 * x^72 + 5 * x^73 - 9 * x^74 - 4 * x^76 + 6 * x^77 - 11 * x^78 + 2 * x^79 - 4 * x^80 + 11 * x^81 - 15 * x^82 + 3 * x^83 - 6 * x^84 + 11 * x^85 - 13 * x^86 + 6 * x^87 - 7 * x^88 + 11 * x^89 - 10 * x^90 + 6 * x^91 - 7 * x^92 + 12 * x^93 - 11 * x^94 + 5 * x^95 - 2 * x^96 + 10 * x^97 - 8 * x^98 + 5 * x^99 - 4 * x^100 + 8 * x^101 - 5 * x^102 + 3 * x^103 - 2 * x^104 + 7 * x^105 - 4 * x^106 + x^107 - x^108 + 4 * x^109 - 4 * x^110 + x^111 + 2 * x^113 - 2 * x^114 - x^116 + x^117 - 2 * x^118 - x^119 + x^120 + x^121 - x^122 - x^126 - x^127 + x^128 + x^129) g(x) = (1 - (10 * x^1/[2]) + (x^4/[2,4] + 8 * x^3/[2,3] + 36 * x^2/[2,2]) - (x^9/[2,4,6] + 8 * x^6/[2,3,4] + 7 * x^5/[2,2,4] + 47 * x^4/[2,2,3] + 57 * x^3/[2,2,2]) + (x^12/[2,4,4,6] + x^16/[2,4,6,8] + 7 * x^10/[2,3,4,5] + 6 * x^7/[2,2,3,4] + 13 * x^6/[2,2,3,3] + 6 * x^10/[2,2,4,6] + 38 * x^7/[2,2,3,4] + 15 * x^6/[2,2,2,4] + 84 * x^5/[2,2,2,3] + 39 * x^4/[2,2,2,2]) - (2 * x^20/[2,4,5,6,8] + x^25/[2,4,6,8,10] + 5 * x^15/[2,3,4,5,6] + 6 * x^10/[2,2,3,4,4] + 5 * x^12/[2,2,3,4,6] + 19 * x^9/[2,2,3,3,4] + 4 * x^13/[2,2,4,4,6] + 5 * x^17/[2,2,4,6,8] + 27 * x^11/[2,2,3,4,5] + 18 * x^8/[2,2,2,3,4] + 30 * x^7/[2,2,2,3,3] + 10 * x^11/[2,2,2,4,6] + 47 * x^8/[2,2,2,3,4] + 11 * x^7/[2,2,2,2,4] + 53 * x^6/[2,2,2,2,3] + 9 * x^5/[2,2,2,2,2]) + (x^36/[2,5,6,8,9,12] + x^30/[2,4,6,6,8,10] + x^16/[2,2,4,4,4,6] + x^36/[2,4,6,8,10,12] + 4 * x^21/[2,3,4,5,6,7] + 5 * x^14/[2,2,3,4,4,5] + 5 * x^15/[2,2,3,4,4,6] + 6 * x^12/[2,2,3,3,4,4] + 2 * x^15/[2,2,3,4,4,6] + 4 * x^19/[2,2,3,4,6,8] + 11 * x^13/[2,2,3,3,4,5] + 4 * x^10/[2,2,2,3,3,4] + x^9/[2,2,2,3,3,3] + 7 * x^21/[2,2,4,5,6,8] + 4 * x^26/[2,2,4,6,8,10] + 13 * x^16/[2,2,3,4,5,6] + 11 * x^11/[2,2,2,3,4,4] + 10 * x^13/[2,2,2,3,4,6] + 25 * x^10/[2,2,2,3,3,4] + 3 * x^14/[2,2,2,4,4,6] + 6 * x^18/[2,2,2,4,6,8] + 24 * x^12/[2,2,2,3,4,5] + 12 * x^9/[2,2,2,2,3,4] + 18 * x^8/[2,2,2,2,3,3] + 5 * x^12/[2,2,2,2,4,6] + 15 * x^9/[2,2,2,2,3,4] + 2 * x^8/[2,2,2,2,2,4] + 9 * x^7/[2,2,2,2,2,3]) - (x^63/[2,6,8,10,12,14,18] + x^42/[2,4,6,7,8,10,12] + 2 * x^24/[2,2,4,4,5,6,8] + x^49/[2,4,6,8,10,12,14] + x^21/[2,2,4,4,4,6,6] + 3 * x^28/[2,3,4,5,6,7,8] + 3 * x^19/[2,2,3,4,4,5,6] + 4 * x^19/[2,2,3,4,4,5,6] + x^18/[2,2,3,4,4,4,6] + 4 * x^22/[2,2,3,4,4,6,8] + 5 * x^16/[2,2,3,3,4,4,5] + 3 * x^23/[2,2,3,4,5,6,8] + 3 * x^28/[2,2,3,4,6,8,10] + 2 * x^18/[2,2,3,3,4,5,6] + 3 * x^13/[2,2,2,3,3,4,4] + x^15/[2,2,2,3,3,4,6] + 3 * x^37/[2,2,5,6,8,9,12] + 2 * x^31/[2,2,4,6,6,8,10] + x^17/[2,2,2,4,4,4,6] + 3 * x^37/[2,2,4,6,8,10,12] + 6 * x^22/[2,2,3,4,5,6,7] + 5 * x^15/[2,2,2,3,4,4,5] + 4 * x^16/[2,2,2,3,4,4,6] + 3 * x^13/[2,2,2,3,3,4,4] + x^16/[2,2,2,3,4,4,6] + 4 * x^20/[2,2,2,3,4,6,8] + 10 * x^14/[2,2,2,3,3,4,5] + 3 * x^11/[2,2,2,2,3,3,4] + x^10/[2,2,2,2,3,3,3] + 4 * x^22/[2,2,2,4,5,6,8] + 3 * x^27/[2,2,2,4,6,8,10] + 6 * x^17/[2,2,2,3,4,5,6] + 3 * x^12/[2,2,2,2,3,4,4] + 5 * x^14/[2,2,2,2,3,4,6] + 6 * x^11/[2,2,2,2,3,3,4] + 2 * x^19/[2,2,2,2,4,6,8] + 4 * x^13/[2,2,2,2,3,4,5] + x^10/[2,2,2,2,2,3,4] + 2 * x^9/[2,2,2,2,2,3,3]) + (x^120/[2,8,12,14,18,20,24,30] + x^40/[2,2,4,5,6,8,9,12] + x^56/[2,4,6,8,8,10,12,14] + x^34/[2,2,4,4,6,6,8,10] + 2 * x^64/[2,4,6,8,10,12,14,16] + x^28/[2,2,4,4,4,6,6,8] + 2 * x^29/[2,2,4,4,5,6,6,8] + x^36/[2,3,4,5,6,7,8,9] + x^25/[2,2,3,4,4,5,6,7] + x^24/[2,2,3,4,4,5,6,6] + 2 * x^26/[2,2,3,4,4,5,6,8] + x^20/[2,2,3,3,4,4,5,5] + x^26/[2,2,3,4,4,5,6,8] + 2 * x^31/[2,2,3,4,4,6,8,10] + x^39/[2,2,3,5,6,8,9,12] + x^39/[2,2,3,4,6,8,10,12] + x^17/[2,2,2,3,3,4,4,5] + 2 * x^64/[2,2,6,8,10,12,14,18] + x^43/[2,2,4,6,7,8,10,12] + x^25/[2,2,2,4,4,5,6,8] + x^50/[2,2,4,6,8,10,12,14] + 2 * x^29/[2,2,3,4,5,6,7,8] + x^20/[2,2,2,3,4,4,5,6] + 2 * x^20/[2,2,2,3,4,4,5,6] + x^23/[2,2,2,3,4,4,6,8] + x^17/[2,2,2,3,3,4,4,5] + x^24/[2,2,2,3,4,5,6,8] + 2 * x^29/[2,2,2,3,4,6,8,10] + x^19/[2,2,2,3,3,4,5,6] + x^14/[2,2,2,2,3,3,4,4] + x^16/[2,2,2,2,3,3,4,6] + x^38/[2,2,2,5,6,8,9,12] + 2 * x^38/[2,2,2,4,6,8,10,12] + x^23/[2,2,2,3,4,5,6,7] + x^21/[2,2,2,2,3,4,6,8] + x^15/[2,2,2,2,3,3,4,5]) - (x^67/[2,2,4,6,8,10,12,14,18] + x^81/[2,4,6,8,10,12,14,16,18] + x^36/[2,2,4,4,5,6,6,8,8] + x^45/[2,2,4,5,6,6,8,9,12] + x^35/[2,2,3,4,4,5,6,8,10] + x^121/[2,2,8,12,14,18,20,24,30] + x^65/[2,2,4,6,8,10,12,14,16] + x^40/[2,2,2,3,4,6,8,10,12]))^-1; Growth rate: 1.2907482365217078702254980946680525922 Perron number: yes Pisot number: no Salem number: no