The Birkhoff-polytope of doubly stochastic 4-by-4 matrices, in its full-dimensional incarnation.
DIM
9
VERTICES
1 0 1 0 0 0 1 0 0 0
1 0 0 1 0 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 0 1 1 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0
1 0 1 0 1 0 0 0 0 0
1 0 1 0 0 0 0 0 0 1
1 0 0 1 0 0 0 0 1 0
1 1 0 0 0 0 0 0 0 1
1 0 0 1 0 0 0 1 0 0
1 1 0 0 0 0 0 0 1 0
1 0 1 0 0 0 0 1 0 0
1 0 0 0 0 1 0 1 0 0
1 0 0 0 1 0 0 0 1 0
1 1 0 0 0 0 1 0 1 0
1 0 1 0 0 0 1 1 0 0
1 1 0 0 0 1 0 0 0 1
1 0 1 0 1 0 0 0 0 1
1 0 0 0 0 0 1 1 0 0
1 0 0 0 1 0 0 0 0 1
1 0 0 0 0 1 0 0 0 1
1 0 0 0 0 0 1 0 1 0
1 0 0 1 0 1 0 1 0 0
1 0 0 1 1 0 0 0 1 0
IN_EQ_DIM
9
FACETS
0 1 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 1
1 -1 -1 -1 0 0 0 0 0 0
1 0 0 0 -1 -1 -1 0 0 0
1 0 0 0 0 0 0 -1 -1 -1
1 -1 0 0 -1 0 0 -1 0 0
1 0 -1 0 0 -1 0 0 -1 0
1 0 0 -1 0 0 -1 0 0 -1
-2 1 1 1 1 1 1 1 1 1
INEQUALITIES
0 1 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 1
1 -1 -1 -1 0 0 0 0 0 0
1 0 0 0 -1 -1 -1 0 0 0
1 0 0 0 0 0 0 -1 -1 -1
1 -1 0 0 -1 0 0 -1 0 0
1 0 -1 0 0 -1 0 0 -1 0
1 0 0 -1 0 0 -1 0 0 -1
-2 1 1 1 1 1 1 1 1 1
AFFINE_HULL
VERTICES_IN_FACETS
{0 1 3 5 6 7 9 11 12 13 15 17 18 19 20 21 22 23}
{1 2 3 4 7 8 9 10 12 13 14 16 18 19 20 21 22 23}
{0 2 4 5 6 8 10 11 12 13 14 15 16 17 18 19 20 21}
{0 1 2 4 6 7 8 9 10 11 12 14 15 16 18 20 21 22}
{0 2 3 5 6 7 8 9 10 11 13 14 15 17 18 19 21 23}
{1 3 4 5 6 7 8 9 10 11 12 13 16 17 19 20 22 23}
{0 1 2 3 4 5 6 7 8 10 13 14 16 17 19 20 21 23}
{0 1 2 3 4 5 6 8 9 11 12 15 16 17 18 19 20 22}
{0 1 2 3 4 5 7 9 10 11 12 13 14 15 18 21 22 23}
{0 1 2 3 4 5 6 7 8 9 10 11 14 15 16 17 22 23}
{0 1 2 3 4 5 12 13 14 15 16 17 18 19 20 21 22 23}
{6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23}
{2 3 4 5 8 9 10 11 12 13 14 15 16 17 18 19 22 23}
{0 1 4 5 6 7 10 11 12 13 14 15 16 17 20 21 22 23}
{0 1 2 3 6 7 8 9 14 15 16 17 18 19 20 21 22 23}
{0 1 2 3 4 5 6 7 8 9 10 11 12 13 18 19 20 21}
N_VERTICES
24
N_FACETS
16
AMBIENT_DIM
9
VOLUME
9.7001763668430325e-04
_version 1.5.1
_application polytope