Below you find a presentation by boundary curves of a certain special spine of a certain non-geometric manifold obtained by gluing two Seifert manifolds with base surface a disc and two exceptional fibers. These Seifert manifolds have toral boundaries, and the Seifert structures induce coordinate systems on these boundaries. The gluing is along the following matrix, written with respect to those coordinate systems:
1 2 1 1
The spine has 12 vertices, and so 13 cells and 24 edges.
1: 1 1 3 6 -7 -5 -4 2: -1 3 -4 3: 3 5 8 -10 -6 -4 4: 24 -20 -23 -2 5: -2 -2 23 21 -18 -24 6: 23 22 19 15 -14 13 -16 -17 -24 7: 6 11 -12 -9 -5 8: 20 18 -22 21 -22 9: 20 17 -19 -21 10: 18 19 16 -15 -17 11: 9 -8 9 -10 -7 12: 7 11 13 -15 16 -14 -12 -8 13: 10 12 13 -14 -11