A384274
Number of connected components of polyhedra in the quarter cubic honeycomb up to translation, rotation, and reflection of the honeycomb.
Original entry on oeis.org
1, 2, 2, 5, 20, 96, 581, 4079, 31079, 247169, 2018826, 16771564, 141113504, 1199154541, 10274686867
Offset: 0
Cf.
A038119 (cubic honeycomb),
A038181 (bitruncated cubic honeycomb),
A343909 (tetrahedral-octahedral honeycomb),
A384254 (rectified cubic honeycomb).
A384755
Triangle read by rows: T(n,k) is the number of face-connected components of polyhedra with k prisms and n-k truncated cuboctahedra in the omnitruncated cubic honeycomb up to rotation and reflection, 0 <= k <= n.
Original entry on oeis.org
1, 1, 1, 1, 2, 1, 3, 7, 10, 2, 12, 41, 76, 46, 4, 61, 335, 809, 777, 232, 13, 407, 3065, 9512, 12863, 7186, 1206, 39, 3226, 30401, 114516, 204143, 172377, 60421, 6548, 155, 28335, 311782, 1381363, 3054599, 3507278, 1975767, 469525, 36081, 637, 262091, 3260971, 16569719, 43731912
Offset: 0
0 | 1;
1 | 1, 1;
2 | 1, 2, 1;
3 | 3, 7, 10, 2;
4 | 12, 41, 76, 46, 4;
5 | 61, 335, 809, 777, 232, 13;
6 | 407, 3065, 9512, 12863, 7186, 1206, 39;
Cf.
A365970 (tetrahedral-octahedral honeycomb),
A384486 (quarter cubic honeycomb),
A384782 (rectified cubic honeycomb).
A384782
Triangle read by rows: T(n,k) is the number of face-connected polyhedral components consisting of k cuboctahedra and n-k octahedra in the rectified cubic honeycomb up to translation, rotation, and reflection of the honeycomb, 0<=k<=n.
Original entry on oeis.org
1, 1, 1, 0, 1, 1, 0, 3, 4, 2, 0, 3, 18, 12, 7, 0, 6, 60, 126, 75, 23, 0, 3, 165, 751, 1025, 473, 112, 0, 3, 346, 3784, 9414, 8936, 3539, 607, 0, 1, 565, 14112, 66503, 108739, 80531, 27027, 3811, 0, 1, 723, 42420, 362939, 994542, 1204093, 725795, 212122, 25413, 0, 0, 723, 101237, 1586479, 7065791, 13389295, 12792264, 6512671, 1678783, 178083
Offset: 0
Table begins:
0 | 1;
1 | 1, 1;
2 | 0, 1, 1;
3 | 0, 3, 4, 2;
4 | 0, 3, 18, 12, 7;
5 | 0, 6, 60, 126, 75, 23;
6 | 0, 3, 165, 751, 1025, 473, 112;
7 | 0, 3, 346, 3784, 9414, 8936, 3539, 607;
8 | 0, 1, 565, 14112, 66503, 108739, 80531, 27027, 3811;
9 | 0, 1, 723, 42420, 362939, 994542, 1204093, 725795, 212122, 25413;
Cf.
A365970 (tetrahedral-octahedral honeycomb),
A384486 (quarter cubic honeycomb),
A384755 (omnitruncated cubic honeycomb).
Showing 1-3 of 3 results.
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