# Anders Björner and Frank H. Lutz. Simplicial manifolds, # bistellar flips and a 16-vertex triangulation # of the Poincaré homology 3-sphere. # Exp. Math. 9, 275-289 (2000). # Anders Björner and Frank H. Lutz. # A 16-vertex triangulation of the Poincaré homology 3-sphere # and non-PL spheres with few vertices. # Electronic Geometry Models, No. 2003.04.001 (2003). Poincare_3_sphere=[ [ 1, 2, 4, 9 ], [ 1, 2, 4, 15 ], [ 1, 2, 6, 14 ], [ 1, 2, 6, 15 ], [ 1, 2, 9, 14 ], [ 1, 3, 4, 12 ], [ 1, 3, 4, 15 ], [ 1, 3, 7, 10 ], [ 1, 3, 7, 12 ], [ 1, 3, 10, 15 ], [ 1, 4, 9, 12 ], [ 1, 5, 6, 13 ], [ 1, 5, 6, 14 ], [ 1, 5, 8, 11 ], [ 1, 5, 8, 13 ], [ 1, 5, 11, 14 ], [ 1, 6, 13, 15 ], [ 1, 7, 8, 10 ], [ 1, 7, 8, 11 ], [ 1, 7, 11, 12 ], [ 1, 8, 10, 13 ], [ 1, 9, 11, 12 ], [ 1, 9, 11, 14 ], [ 1, 10, 13, 15 ], [ 2, 3, 5, 10 ], [ 2, 3, 5, 11 ], [ 2, 3, 7, 10 ], [ 2, 3, 7, 13 ], [ 2, 3, 11, 13 ], [ 2, 4, 9, 13 ], [ 2, 4, 11, 13 ], [ 2, 4, 11, 15 ], [ 2, 5, 8, 11 ], [ 2, 5, 8, 12 ], [ 2, 5, 10, 12 ], [ 2, 6, 10, 12 ], [ 2, 6, 10, 14 ], [ 2, 6, 12, 15 ], [ 2, 7, 9, 13 ], [ 2, 7, 9, 14 ], [ 2, 7, 10, 14 ], [ 2, 8, 11, 15 ], [ 2, 8, 12, 15 ], [ 3, 4, 5, 14 ], [ 3, 4, 5, 15 ], [ 3, 4, 12, 14 ], [ 3, 5, 10, 15 ], [ 3, 5, 11, 14 ], [ 3, 7, 12, 13 ], [ 3, 11, 13, 14 ], [ 3, 12, 13, 14 ], [ 4, 5, 6, 7 ], [ 4, 5, 6, 14 ], [ 4, 5, 7, 15 ], [ 4, 6, 7, 11 ], [ 4, 6, 10, 11 ], [ 4, 6, 10, 14 ], [ 4, 7, 11, 15 ], [ 4, 8, 9, 12 ], [ 4, 8, 9, 13 ], [ 4, 8, 10, 13 ], [ 4, 8, 10, 14 ], [ 4, 8, 12, 14 ], [ 4, 10, 11, 13 ], [ 5, 6, 7, 13 ], [ 5, 7, 9, 13 ], [ 5, 7, 9, 15 ], [ 5, 8, 9, 12 ], [ 5, 8, 9, 13 ], [ 5, 9, 10, 12 ], [ 5, 9, 10, 15 ], [ 6, 7, 11, 12 ], [ 6, 7, 12, 13 ], [ 6, 10, 11, 12 ], [ 6, 12, 13, 15 ], [ 7, 8, 10, 14 ], [ 7, 8, 11, 15 ], [ 7, 8, 14, 15 ], [ 7, 9, 14, 15 ], [ 8, 12, 14, 15 ], [ 9, 10, 11, 12 ], [ 9, 10, 11, 16 ], [ 9, 10, 15, 16 ], [ 9, 11, 14, 16 ], [ 9, 14, 15, 16 ], [ 10, 11, 13, 16 ], [ 10, 13, 15, 16 ], [ 11, 13, 14, 16 ], [ 12, 13, 14, 15 ], [ 13, 14, 15, 16 ] ]