#  July 9, 2008.
#
#  Q-bipartite double of Schlafli graph 
#
#
#  SRG has 
#    [  1   16  10  ]        [ 1    6     20 ]
#P = [  1    4  -5  ]   Q =  [ 1   3/2  -5/2 ]
#    [  1   -2   1  ]        [ 1   -3      2 ]
d := 5;

v := [1, 10, 16, 16, 10, 1]:
verts := 54;

Q := matrix(6,6,[
1,  6,     20,     20,     6,  1,
1,  3,      2,     -2,    -3, -1,
1, 3/2,  -5/2,   -5/2,   3/2,  1,
1,-3/2,  -5/2,    5/2,   3/2, -1,
1, -3,      2,      2,    -3,  1,
1, -6,     20,    -20,     6, -1]);


#  This tridiagonal  matrix, L_1-star,  allows us to fill out the cols of Q
#  if we are only given the cosines (normalized column 1 of Q).
L := matrix([
[0 ,    6  ,   0    ,  0    ,   0    ,  0  ],
[1 ,    0  ,   5    ,  0    ,   0    ,  0  ],
[0 ,   3/2 ,   0    , 9/2   ,   0    ,  0  ],
[0 ,    0  ,  9/2   ,  0    ,  3/2   ,  0  ],
[0 ,    0  ,   0    ,  5    ,   0    ,  1  ],
[0 ,    0  ,   0    ,  0    ,   6    ,  0  ]
]);


 
      [0    10    0    0     0    0]
      [                            ]
      [1     0    8    0     1    0]
      [                            ]
      [0     5    0    5     0    0]
L_1 = [                            ]
      [0     0    5    0     5    0]
      [                            ]
      [0     1    0    8     0    1]
      [                            ]
      [0     0    0    0    10    0]
 
      [0    0    16     0    0    0]
      [                            ]
      [0    8     0     8    0    0]
      [                            ]
      [1    0    10     0    5    0]
L_2 = [                            ]
      [0    5     0    10    0    1]
      [                            ]
      [0    0     8     0    8    0]
      [                            ]
      [0    0     0    16    0    0]
 
      [0    0     0    16    0    0]
      [                            ]
      [0    0     8     0    8    0]
      [                            ]
      [0    5     0    10    0    1]
L_3 = [                            ]
      [1    0    10     0    5    0]
      [                            ]
      [0    8     0     8    0    0]
      [                            ]
      [0    0    16     0    0    0]
 
      [0     0    0    0    10    0]
      [                            ]
      [0     1    0    8     0    1]
      [                            ]
      [0     0    5    0     5    0]
L_4 = [                            ]
      [0     5    0    5     0    0]
      [                            ]
      [1     0    8    0     1    0]
      [                            ]
      [0    10    0    0     0    0]
 
       [0    0    0    0    0    1]
       [                          ]
       [0    0    0    0    1    0]
       [                          ]
       [0    0    0    1    0    0]
 L_5 = [                          ]
       [0    0    1    0    0    0]
       [                          ]
       [0    1    0    0    0    0]
       [                          ]
       [1    0    0    0    0    0]
 


 
      [1     10    16     16    10     1]
      [                                 ]
      [1      5     4     -4    -5    -1]
      [                                 ]
      [1      1    -2     -2     1     1]
 P := [                                 ]
      [1     -1    -2      2     1    -1]
      [                                 ]
      [1     -5     4      4    -5     1]
      [                                 ]
      [1    -10    16    -16    10    -1]

    [1     6       20      20      6      1]
    [                                      ]
    [1     3       2       -2     -3     -1]
    [                                      ]
    [1    3/2     -5/2    -5/2    3/2     1]
Q = [                                      ]
    [1    -3/2    -5/2    5/2     3/2    -1]
    [                                      ]
    [1     -3      2       2      -3      1]
    [                                      ]
    [1     -6      20     -20      6     -1]
 
 
       [0     6      0      0      0     0]
       [                                  ]
       [1     0      5      0      0     0]
       [                                  ]
       [0    3/2     0     9/2     0     0]
 Ls1 = [                                  ]
       [0     0     9/2     0     3/2    0]
       [                                  ]
       [0     0      0      5      0     1]
       [                                  ]
       [0     0      0      0      6     0]
     
      [0     0      20      0       0     0]
      [                                    ]
      [0     5      0       15      0     0]
      [                                    ]
      [1     0     29/2     0      9/2    0]
Ls2 = [                                    ]
      [0    9/2     0      29/2     0     1]
      [                                    ]
      [0     0      15      0       5     0]
      [                                    ]
      [0     0      0       20      0     0]
     
      [0     0      0       20      0     0]
      [                                    ]
      [0     0      15      0       5     0]
      [                                    ]
      [0    9/2     0      29/2     0     1]
Ls3 = [                                    ]
      [1     0     29/2     0      9/2    0]
      [                                    ]
      [0     5      0       15      0     0]
      [                                    ]
      [0     0      20      0       0     0]
     
       [0     0      0      0      6     0]
       [                                  ]
       [0     0      0      5      0     1]
       [                                  ]
       [0     0     9/2     0     3/2    0]
 Ls4 = [                                  ]
       [0    3/2     0     9/2     0     0]
       [                                  ]
       [1     0      5      0      0     0]
       [                                  ]
       [0     6      0      0      0     0]
 
       [0    0    0    0    0    1]
       [                          ]
       [0    0    0    0    1    0]
       [                          ]
       [0    0    0    1    0    0]
 Ls5 = [                          ]
       [0    0    1    0    0    0]
       [                          ]
       [0    1    0    0    0    0]
       [                          ]
       [1    0    0    0    0    0]