[new number](old number), facet, dimension, signature in reflection rep (+,0,-), nu(wt), nu(standard), Levi
old number refers to the order from Stembridge's list
A facet is positive semidefinite if the third entry of the signature is 0
Each facet is labelled by the positive co-roots: -,1,+ mean <1,=1 or >1 respectively.
The Levi factor is the smallest root system containing all coroots for which the value is >=1

[1](12) -,-,-,-,-,-,-,+,+ 3 (3,0,0) (1/4,0,5/8) (7/8,1/4,1/4) 
[2](15) -,-,-,-,-,-,-,-,- 3 (3,0,0) (0,0,0) (0,0,0) 
[3](13) -,-,-,-,-,-,-,1,+ 2 (2,1,0) (1/4,1/4,1/4) (3/4,1/2,1/4) 
[4](10) -,-,-,-,-,-,1,+,+ 2 (2,1,0) (1/4,0,3/4) (1,1/4,1/4) 
[5](11) -,-,-,-,1,-,-,+,+ 2 (2,1,0) (1/2,0,1/4) (3/4,1/2,1/2) 
[6](14) -,-,-,-,-,-,-,-,1 2 (2,1,0) (0,1/4,1/2) (3/4,1/4,0) 
[7](7) -,-,-,-,-,1,1,1,+ 1 (2,1,0) (0,3/4,1/4) (1,3/4,0) 
[8](9) -,-,-,-,1,-,1,+,+ 1 (1,2,0) (1/4,1/2,1/4) (1,3/4,1/4) 
[9](3) -,-,-,-,1,-,-,1,+ 1 (2,1,0) (1/4,1/2,0) (3/4,3/4,1/4) 
[10](5) -,-,-,-,-,-,-,1,1 1 (2,1,0) (1/4,0,1/2) (3/4,1/4,1/4) 
[11](4) -,-,1,-,-,1,1,1,1 0 (2,1,0) (0,0,1) (1,0,0) 
[12](2) -,1,-,1,1,1,1,1,+ 0 (1,2,0) (0,1,0) (1,1,0) 
[13](1) -,-,-,-,1,-,-,1,1 0 (2,1,0) (1/2,0,0) (1/2,1/2,1/2) 
[14](8) 1,1,1,+,+,+,+,+,+ 0 (0,3,0) (1,1,1) (3,2,1) 
[15](6) -,1,1,1,1,+,+,+,+ 0 (1,2,0) (0,1,1) (2,1,0) 


Closed Regions (old numbering/dimension):
Closure of facet (12/3): (13/2),(10/2),(11/2),(7/1),(9/1),(3/1),(5/1),(4/0),(2/0),(1/0)
Closure of facet (15/3): (14/2),(5/1),(4/0),(1/0)
Closure of facet (8/0): 
Closure of facet (6/0): 

Closed Regions (new numbering/dimension):
Closure of facet [1/3]: [3/2],[4/2],[5/2],[7/1],[8/1],[9/1],[10/1],[11/0],[12/0],[13/0]
Closure of facet [2/3]: [6/2],[10/1],[11/0],[13/0]
Closure of facet [14/0]: 
Closure of facet [15/0]: 

Boundaries (new numbering/dimension):
row labelled [i] gives boundary of facet [i]

[1/3] [3/2][4/2][5/2][7/1][8/1][9/1][10/1][11/0][12/0][13/0]
[2/3] [6/2][10/1][11/0][13/0]
[3/2] [7/1][9/1][10/1][11/0][12/0][13/0]
[4/2] [7/1][8/1][11/0][12/0]
[5/2] [8/1][9/1][12/0][13/0]
[6/2] [10/1][11/0][13/0]
[7/1] [11/0][12/0]
[8/1] [12/0]
[9/1] [12/0][13/0]
[10/1] [11/0][13/0]
[11/0] 
[12/0] 
[13/0] 
[14/0] 
[15/0] 

Boundaries (old numbering/dimension):
row labelled (i) gives boundary of facet (i)

(1/0) 
(2/0) 
(3/1) (1/0)(2/0)
(4/0) 
(5/1) (1/0)(4/0)
(6/0) 
(7/1) (2/0)(4/0)
(8/0) 
(9/1) (2/0)
(10/2) (2/0)(4/0)(7/1)(9/1)
(11/2) (1/0)(2/0)(3/1)(9/1)
(12/3) (1/0)(2/0)(3/1)(4/0)(5/1)(7/1)(9/1)(10/2)(11/2)(13/2)
(13/2) (1/0)(2/0)(3/1)(4/0)(5/1)(7/1)
(14/2) (1/0)(4/0)(5/1)
(15/3) (1/0)(4/0)(5/1)(14/2)

Co-Boundaries (new numbering/dimension):
row labelled [i] gives facets with [i] on the boundary.
[1/3] 
[2/3] 
[3/2] [1/3]
[4/2] [1/3]
[5/2] [1/3]
[6/2] [2/3]
[7/1] [1/3][3/2][4/2]
[8/1] [1/3][4/2][5/2]
[9/1] [1/3][3/2][5/2]
[10/1] [1/3][2/3][3/2][6/2]
[11/0] [1/3][2/3][3/2][4/2][6/2][7/1][10/1]
[12/0] [1/3][3/2][4/2][5/2][7/1][8/1][9/1]
[13/0] [1/3][2/3][3/2][5/2][6/2][9/1][10/1]
[14/0] 
[15/0] 

Co-Boundaries (old numbering):
row labelled (i) gives facets with (i) on the boundary.
(1/0) (3/1)(5/1)(11/2)(12/3)(13/2)(14/2)(15/3)
(2/0) (3/1)(7/1)(9/1)(10/2)(11/2)(12/3)(13/2)
(3/1) (11/2)(12/3)(13/2)
(4/0) (5/1)(7/1)(10/2)(12/3)(13/2)(14/2)(15/3)
(5/1) (12/3)(13/2)(14/2)(15/3)
(6/0) 
(7/1) (10/2)(12/3)(13/2)
(8/0) 
(9/1) (10/2)(11/2)(12/3)
(10/2) (12/3)
(11/2) (12/3)
(12/3) 
(13/2) (12/3)
(14/2) (15/3)
(15/3) 

Connected Components: (new numbering/dimension)
[1/3][2/3][3/2][4/2][5/2][6/2][7/1][8/1][9/1][10/1][11/0][12/0][13/0]
[14/0]
[15/0]