Description of the boundary

Below you find a description of the induced cell decomposition of the boundary of a regular neighborhood of this spine:

Boundary is connected - Sphere

Boundary cells:
Component 1
1+ = { 1_1, 6_3, 12_3, -13_1, 16_3, -17_1, -11_3, -7_1, -3_1 }
3+ = { 1_1, 5_2, -6_1, -2_2 }
5- = { 5_2, 12_1, -14_3, -10_2, -6_3 }
9- = { 10_2, 17_2, -18_3, -12_3 }
2- = { 2_3, 5_1, 10_1, -11_2, 15_1, -18_3, -13_1, -8_3, -4_3 }
10- = { 7_2, 15_2, -16_3, -8_3 }
8- = { 13_2, -14_2, 17_1, -15_2, 9_3 }
7+ = { 11_3, 14_2, 18_1, -16_2, -9_1 }
6+ = { 3_3, 8_2, -9_1, -7_1, -4_2 }
4+ = { 1_3, -2_2, 3_1, -4_2 }
1- = { 1_3, 6_1, 12_1, -13_3, 16_1, -17_3, -11_1, -7_3, -3_3 }
8+ = { 13_3, -14_3, 17_2, -15_1, 9_2 }
4- = { 1_2, -2_3, 3_2, -4_1 }
3- = { 1_2, 5_1, -6_2, -2_1 }
5+ = { 5_3, 12_2, -14_1, -10_1, -6_2 }
7- = { 11_2, 14_1, 18_2, -16_1, -9_2 }
6- = { 3_2, 8_1, -9_3, -7_2, -4_3 }
2+ = { 2_1, 5_3, 10_3, -11_1, 15_3, -18_1, -13_2, -8_1, -4_1 }
10+ = { 7_3, 15_3, -16_2, -8_2 }
9+ = { 10_3, 17_3, -18_2, -12_2 }

The meaning of these data is as follows. A regular neighborhood of a special spine P is equipped with a natural retraction onto P such that the pre-image of every 2-cell consists of two 2-cells, the pre-image of each edge, of three edges, and the pre-image of each vertex, of four vertices. The pre-images of the j-th edge are numbered j_1, j_2, and j_3. The orientations of these edges are such that the retraction be orientation-preserving. The two pre-images of i-th cell are denoted "i+" and "i-". Again, the orientation of a cell must be preserved by the retraction. Each cell is given by the sequence of oriented edges along which it passes, similar to presentation of cells of a spine by their boundary curves.