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steiner triples see this wikipedia page . n = 3: {{0, 1, 2}} n = 7: {{0, 1, 3}, {0, 2, 4}, {0, 5, 6}, {1, 2, 6}, {1, 4, 5}, {2, 3, 5}, {3, 4, 6}} n = 9: {{0, 1, 5}, {0, 2, 4}, {0, 3, 6}, {0, 7, 8}, {1, 2, 3}, {1, 4, 7}, {1, 6, 8}, {2, 5, 8}, {2, 6, 7}, {3, 4, 8}, {3, 5, 7}, {4, 5, 6}} n = 13: {{0, 1, 6}, {0, 2, 5}, {0, 3, 7}, {0, 4, 8}, {0, 9, 11}, {0, 10, 12}, {1, 2, 7}, {1, 3, 4}, {1, 5, 9}, {1, 8, 10}, {1, 11, 12}, {2, 3, 6}, {2, 4, 12}, {2, 8, 9}, {2, 10, 11}, {3, 5, 12}, {3, 8, 11}, {3, 9, 10}, {4, 5, 10}, {4, 6, 9}, {4, 7, 11}, {5, 6, 11}, {5, 7, 8}, {6, 7, 10}, {6, 8, 12}, {7, 9, 12}} n = 15: {{0, 1, 8}, {0, 2, 6}, {0, 3, 9}, {0, 4, 7}, {0, 5, 10}, {0, 11, 14}, {0, 12, 13}, {1, 2, 9}, {1, 3, 7}, {1, 4, 5}, {1, 6, 11}, {1, 10, 12}, {1, 13, 14}, {2, 3, 5}, {2, 4, 8}, {2, 7, 12}, {2, 10, 14}, {2, 11, 13}, {3, 4, 6}, {3, 8, 13}, {3, 10, 11}, {3, 12, 14}, {4, 9, 14}, {4, 10, 13}, {4, 11, 12}, {5, 6, 13}, {5, 7, 11}, {5, 8, 14}, {5, 9, 12}, {6, 7, 14}, {6, 8, 12}, {6, 9, 10}, {7, 8, 10}, {7, 9, 13}, {8, 9, 11}} n = 19: {{0, 1, 9}, {0, 2, 7}, {0, 3, 10}, {0, 4, 8}, {0, 5, 11}, {0, 6, 12}, {0, 13, 17}, {0, 14, 16}, {0, 15, 18}, {1, 2, 10}, {1, 3, 8}, {1, 4, 11}, {1, 5, 6}, {1, 7, 13}, {1, 12, 14}, {1, 15, 17}, {1, 16, 18}, {2, 3, 11}, {2, 4, 6}, {2, 5, 9}, {2, 8, 14}, {2, 12, 16}, {2, 13, 15}, {2, 17, 18}, {3, 4, 9}, {3, 5, 7}, {3, 6, 18}, {3, 12, 13}, {3, 14, 17}, {3, 15, 16}, {4, 5, 10}, {4, 7, 18}, {4, 12, 15}, {4, 13, 14}, {4, 16, 17}, {5, 8, 18}, {5, 12, 17}, {5, 13, 16}, {5, 14, 15}, {6, 7, 15}, {6, 8, 13}, {6, 9, 16}, {6, 10, 14}, {6, 11, 17}, {7, 8, 16}, {7, 9, 14}, {7, 10, 17}, {7, 11, 12}, {8, 9, 17}, {8, 10, 12}, {8, 11, 15}, {9, 10, 15}, {9, 11, 13}, {9, 12, 18}, {10, 11, 16}, {10, 13, 18}, {11, 14, 18}} n = 21: {{0, 1, 11}, {0, 2, 8}, {0, 3, 12}, {0, 4, 9}, {0, 5, 13}, {0, 6, 10}, {0, 7, 14}, {0, 15, 20}, {0, 16, 19}, {0, 17, 18}, {1, 2, 12}, {1, 3, 9}, {1, 4, 13}, {1, 5, 10}, {1, 6, 7}, {1, 8, 15}, {1, 14, 16}, {1, 17, 20}, {1, 18, 19}, {2, 3, 13}, {2, 4, 10}, {2, 5, 7}, {2, 6, 11}, {2, 9, 16}, {2, 14, 18}, {2, 15, 17}, {2, 19, 20}, {3, 4, 7}, {3, 5, 11}, {3, 6, 8}, {3, 10, 17}, {3, 14, 20}, {3, 15, 19}, {3, 16, 18}, {4, 5, 8}, {4, 6, 12}, {4, 11, 18}, {4, 14, 15}, {4, 16, 20}, {4, 17, 19}, {5, 6, 9}, {5, 12, 19}, {5, 14, 17}, {5, 15, 16}, {5, 18, 20}, {6, 13, 20}, {6, 14, 19}, {6, 15, 18}, {6, 16, 17}, {7, 8, 18}, {7, 9, 15}, {7, 10, 19}, {7, 11, 16}, {7, 12, 20}, {7, 13, 17}, {8, 9, 19}, {8, 10, 16}, {8, 11, 20}, {8, 12, 17}, {8, 13, 14}, {9, 10, 20}, {9, 11, 17}, {9, 12, 14}, {9, 13, 18}, {10, 11, 14}, {10, 12, 18}, {10, 13, 15}, {11, 12, 15}, {11, 13, 19}, {12, 13, 16}} n = 25: {{0, 1, 12}, {0, 2, 9}, {0, 3, 13}, {0, 4, 10}, {0, 5, 14}, {0, 6, 11}, {0, 7, 15}, {0, 8, 16}, {0, 17, 23}, {0, 18, 22}, {0, 19, 21}, {0, 20, 24}, {1, 2, 13}, {1, 3, 10}, {1, 4, 14}, {1, 5, 11}, {1, 6, 15}, {1, 7, 8}, {1, 9, 17}, {1, 16, 18}, {1, 19, 23}, {1, 20, 22}, {1, 21, 24}, {2, 3, 14}, {2, 4, 11}, {2, 5, 15}, {2, 6, 8}, {2, 7, 12}, {2, 10, 18}, {2, 16, 20}, {2, 17, 19}, {2, 21, 23}, {2, 22, 24}, {3, 4, 15}, {3, 5, 8}, {3, 6, 12}, {3, 7, 9}, {3, 11, 19}, {3, 16, 22}, {3, 17, 21}, {3, 18, 20}, {3, 23, 24}, {4, 5, 12}, {4, 6, 9}, {4, 7, 13}, {4, 8, 24}, {4, 16, 17}, {4, 18, 23}, {4, 19, 22}, {4, 20, 21}, {5, 6, 13}, {5, 7, 10}, {5, 9, 24}, {5, 16, 19}, {5, 17, 18}, {5, 20, 23}, {5, 21, 22}, {6, 7, 14}, {6, 10, 24}, {6, 16, 21}, {6, 17, 20}, {6, 18, 19}, {6, 22, 23}, {7, 11, 24}, {7, 16, 23}, {7, 17, 22}, {7, 18, 21}, {7, 19, 20}, {8, 9, 20}, {8, 10, 17}, {8, 11, 21}, {8, 12, 18}, {8, 13, 22}, {8, 14, 19}, {8, 15, 23}, {9, 10, 21}, {9, 11, 18}, {9, 12, 22}, {9, 13, 19}, {9, 14, 23}, {9, 15, 16}, {10, 11, 22}, {10, 12, 19}, {10, 13, 23}, {10, 14, 16}, {10, 15, 20}, {11, 12, 23}, {11, 13, 16}, {11, 14, 20}, {11, 15, 17}, {12, 13, 20}, {12, 14, 17}, {12, 15, 21}, {12, 16, 24}, {13, 14, 21}, {13, 15, 18}, {13, 17, 24}, {14, 15, 22}, {14, 18, 24}, {15, 19, 24}} n = 27: {{0, 1, 14}, {0, 2, 10}, {0, 3, 15}, {0, 4, 11}, {0, 5, 16}, {0, 6, 12}, {0, 7, 17}, {0, 8, 13}, {0, 9, 18}, {0, 19, 26}, {0, 20, 25}, {0, 21, 24}, {0, 22, 23}, {1, 2, 15}, {1, 3, 11}, {1, 4, 16}, {1, 5, 12}, {1, 6, 17}, {1, 7, 13}, {1, 8, 9}, {1, 10, 19}, {1, 18, 20}, {1, 21, 26}, {1, 22, 25}, {1, 23, 24}, {2, 3, 16}, {2, 4, 12}, {2, 5, 17}, {2, 6, 13}, {2, 7, 9}, {2, 8, 14}, {2, 11, 20}, {2, 18, 22}, {2, 19, 21}, {2, 23, 26}, {2, 24, 25}, {3, 4, 17}, {3, 5, 13}, {3, 6, 9}, {3, 7, 14}, {3, 8, 10}, {3, 12, 21}, {3, 18, 24}, {3, 19, 23}, {3, 20, 22}, {3, 25, 26}, {4, 5, 9}, {4, 6, 14}, {4, 7, 10}, {4, 8, 15}, {4, 13, 22}, {4, 18, 26}, {4, 19, 25}, {4, 20, 24}, {4, 21, 23}, {5, 6, 10}, {5, 7, 15}, {5, 8, 11}, {5, 14, 23}, {5, 18, 19}, {5, 20, 26}, {5, 21, 25}, {5, 22, 24}, {6, 7, 11}, {6, 8, 16}, {6, 15, 24}, {6, 18, 21}, {6, 19, 20}, {6, 22, 26}, {6, 23, 25}, {7, 8, 12}, {7, 16, 25}, {7, 18, 23}, {7, 19, 22}, {7, 20, 21}, {7, 24, 26}, {8, 17, 26}, {8, 18, 25}, {8, 19, 24}, {8, 20, 23}, {8, 21, 22}, {9, 10, 23}, {9, 11, 19}, {9, 12, 24}, {9, 13, 20}, {9, 14, 25}, {9, 15, 21}, {9, 16, 26}, {9, 17, 22}, {10, 11, 24}, {10, 12, 20}, {10, 13, 25}, {10, 14, 21}, {10, 15, 26}, {10, 16, 22}, {10, 17, 18}, {11, 12, 25}, {11, 13, 21}, {11, 14, 26}, {11, 15, 22}, {11, 16, 18}, {11, 17, 23}, {12, 13, 26}, {12, 14, 22}, {12, 15, 18}, {12, 16, 23}, {12, 17, 19}, {13, 14, 18}, {13, 15, 23}, {13, 16, 19}, {13, 17, 24}, {14, 15, 19}, {14, 16, 24}, {14, 17, 20}, {15, 16, 20}, {15, 17, 25}, {16, 17, 21}} n = 31: {{0, 1, 15}, {0, 2, 11}, {0, 3, 16}, {0, 4, 12}, {0, 5, 17}, {0, 6, 13}, {0, 7, 18}, {0, 8, 14}, {0, 9, 19}, {0, 10, 20}, {0, 21, 29}, {0, 22, 28}, {0, 23, 27}, {0, 24, 26}, {0, 25, 30}, {1, 2, 16}, {1, 3, 12}, {1, 4, 17}, {1, 5, 13}, {1, 6, 18}, {1, 7, 14}, {1, 8, 19}, {1, 9, 10}, {1, 11, 21}, {1, 20, 22}, {1, 23, 29}, {1, 24, 28}, {1, 25, 27}, {1, 26, 30}, {2, 3, 17}, {2, 4, 13}, {2, 5, 18}, {2, 6, 14}, {2, 7, 19}, {2, 8, 10}, {2, 9, 15}, {2, 12, 22}, {2, 20, 24}, {2, 21, 23}, {2, 25, 29}, {2, 26, 28}, {2, 27, 30}, {3, 4, 18}, {3, 5, 14}, {3, 6, 19}, {3, 7, 10}, {3, 8, 15}, {3, 9, 11}, {3, 13, 23}, {3, 20, 26}, {3, 21, 25}, {3, 22, 24}, {3, 27, 29}, {3, 28, 30}, {4, 5, 19}, {4, 6, 10}, {4, 7, 15}, {4, 8, 11}, {4, 9, 16}, {4, 14, 24}, {4, 20, 28}, {4, 21, 27}, {4, 22, 26}, {4, 23, 25}, {4, 29, 30}, {5, 6, 15}, {5, 7, 11}, {5, 8, 16}, {5, 9, 12}, {5, 10, 30}, {5, 20, 21}, {5, 22, 29}, {5, 23, 28}, {5, 24, 27}, {5, 25, 26}, {6, 7, 16}, {6, 8, 12}, {6, 9, 17}, {6, 11, 30}, {6, 20, 23}, {6, 21, 22}, {6, 24, 29}, {6, 25, 28}, {6, 26, 27}, {7, 8, 17}, {7, 9, 13}, {7, 12, 30}, {7, 20, 25}, {7, 21, 24}, {7, 22, 23}, {7, 26, 29}, {7, 27, 28}, {8, 9, 18}, {8, 13, 30}, {8, 20, 27}, {8, 21, 26}, {8, 22, 25}, {8, 23, 24}, {8, 28, 29}, {9, 14, 30}, {9, 20, 29}, {9, 21, 28}, {9, 22, 27}, {9, 23, 26}, {9, 24, 25}, {10, 11, 25}, {10, 12, 21}, {10, 13, 26}, {10, 14, 22}, {10, 15, 27}, {10, 16, 23}, {10, 17, 28}, {10, 18, 24}, {10, 19, 29}, {11, 12, 26}, {11, 13, 22}, {11, 14, 27}, {11, 15, 23}, {11, 16, 28}, {11, 17, 24}, {11, 18, 29}, {11, 19, 20}, {12, 13, 27}, {12, 14, 23}, {12, 15, 28}, {12, 16, 24}, {12, 17, 29}, {12, 18, 20}, {12, 19, 25}, {13, 14, 28}, {13, 15, 24}, {13, 16, 29}, {13, 17, 20}, {13, 18, 25}, {13, 19, 21}, {14, 15, 29}, {14, 16, 20}, {14, 17, 25}, {14, 18, 21}, {14, 19, 26}, {15, 16, 25}, {15, 17, 21}, {15, 18, 26}, {15, 19, 22}, {15, 20, 30}, {16, 17, 26}, {16, 18, 22}, {16, 19, 27}, {16, 21, 30}, {17, 18, 27}, {17, 19, 23}, {17, 22, 30}, {18, 19, 28}, {18, 23, 30}, {19, 24, 30}} n = 33: {{0, 1, 17}, {0, 2, 12}, {0, 3, 18}, {0, 4, 13}, {0, 5, 19}, {0, 6, 14}, {0, 7, 20}, {0, 8, 15}, {0, 9, 21}, {0, 10, 16}, {0, 11, 22}, {0, 23, 32}, {0, 24, 31}, {0, 25, 30}, {0, 26, 29}, {0, 27, 28}, {1, 2, 18}, {1, 3, 13}, {1, 4, 19}, {1, 5, 14}, {1, 6, 20}, {1, 7, 15}, {1, 8, 21}, {1, 9, 16}, {1, 10, 11}, {1, 12, 23}, {1, 22, 24}, {1, 25, 32}, {1, 26, 31}, {1, 27, 30}, {1, 28, 29}, {2, 3, 19}, {2, 4, 14}, {2, 5, 20}, {2, 6, 15}, {2, 7, 21}, {2, 8, 16}, {2, 9, 11}, {2, 10, 17}, {2, 13, 24}, {2, 22, 26}, {2, 23, 25},