# MAPLE.   April 1, 2010
# 
# Open parameter set from Van Dam thesis
#
d := 3;

v := [1 ,  20 ,  30 ,  40 ]:
verts := 91;


Q := matrix([
[1 ,   12   ,   65   ,   13  ],
[1 ,  21/5  ,    0   , -26/5 ],
[1 ,   8/5  , -13/2  ,  39/10],
[1 , -18/5 ,   13/4  , -13/20]
]);



#  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 ,     12    ,     0      ,    0    ],
[1 ,   47/35   ,  338/35    ,    0    ],
[0 ,  312/175  ,  303/35    ,  39/25  ],
[0 ,      0    ,   39/5     ,  21/5   ]
]);


       [0    20     0     0]
       [                   ]
       [1     3    12     4]
 L1 := [                   ]
       [0     8     4     8]
       [                   ]
       [0     2     6    12]

       [0     0    30     0]
       [                   ]
       [0    12     6    12]
 L2 := [                   ]
       [1     4    13    12]
       [                   ]
       [0     6     9    15]

       [0     0     0    40]
       [                   ]
       [0     4    12    24]
 L3 := [                   ]
       [0     8    12    20]
       [                   ]
       [1    12    15    12]


       [1    20    30     40]
       [                    ]
       [1     7     4    -12]
  P := [                    ]
       [1     0    -3      2]
       [                    ]
       [1    -8     9     -2]

       [1     12       65       13  ]
       [                            ]
       [1    21/5       0      -26/5]
  Q := [                            ]
       [                        39  ]
       [1     8/5     -13/2     --  ]
       [                        10  ]
       [                            ]
       [                        -13 ]
       [1    -18/5    13/4      --- ]
       [                        20  ]

       [0    12      0       0  ]
       [                        ]
       [     47     338         ]
       [1    --     ---      0  ]
       [     35     35          ]
Ls1 := [                        ]
       [     312    303      39 ]
       [0    ---    ---      -- ]
       [     175    35       25 ]
       [                        ]
       [0     0     39/5    21/5]

       [0     0       65       0 ]
       [                         ]
       [     338     1313     169]
       [0    ---     ----     ---]
       [     35       28      20 ]
Ls2 := [                         ]
       [     303     2535     403]
       [1    ---     ----     ---]
       [     35       56      40 ]
       [                         ]
       [                      273]
       [0    39/5    403/8    ---]
       [                      40 ]

       [0     0       0     13 ]
       [                       ]
       [             169    91 ]
       [0     0      ---    -- ]
       [             20     20 ]
Ls3 := [                       ]
       [      39     403    273]
       [0     --     ---    ---]
       [      25     40     200]
       [                       ]
       [             273    39 ]
       [1    21/5    ---    -- ]
       [             40     40 ]