From deloera@math.ucdavis.edu Thu Jan 30 15:33:02 2003
Date: Thu, 30 Jan 2003 15:08:22 -0800 (PST)
From: Jesus De Loera <deloera@math.ucdavis.edu>
To: kittens@math.ucdavis.edu
Cc: ramon@math.ucdavis.edu
Subject: More test cases (fwd)


Hickerson knows the answer for all these polytopes...
we should be able to get it...

-- 

---------- Forwarded message ----------
Date: Thu, 30 Jan 2003 13:46:07 -0800
From: Dean Hickerson <dean@math.ucdavis.edu>
To: deloera@math.ucdavis.edu
Subject: More test cases

Jesus:  Here are the other cases for which I know the answer, between the
first and second examples from my previous message.  I hope this is helpful
to you.

Dean Hickerson
dean@math.ucdavis.edu


----------------------  m = 7.  8 lattice points.
4 4
0 1 1 1
24 13 -11 -23
24 -11 -23 13
24 -23 13 -11
----------------------  m = 8.  22 lattice points.
5 5
1 2 2 2 1
1 -1 2 -1 1
4 -1 -4 -1 4
16 11 -4 -13 -8
16 -13 -4 11 -8
----------------------  m = 9.  9 lattice points.
5 5
0 1 1 1 1
1 -1 -1 3 -1
13 11 -1 -9 -13
13 -1 -13 -9 11
13 -13 11 -9 -1
----------------------  m = 10.  24 lattice points.
6 6
1 2 2 2 2 1
2 -2 4 -2 4 -1
25 2 -22 -22 2 25
25 -22 2 2 -22 25
50 46 4 -26 -44 -25
50 -26 -44 46 4 -25
----------------------  m = 11.  12 lattice points.
6 6
0 1 1 1 1 1
60 61 13 -23 -47 -59
60 13 -47 -59 -23 61
60 -23 -59 13 61 -47
60 -47 -23 61 -59 13
60 -59 61 -47 13 -23
----------------------  m = 12.  38 lattice points.
7 7
1 2 2 2 2 2 1
1 -1 2 -1 2 -1 1
3 -2 -2 6 -2 -2 3
4 -1 -4 -1 8 -1 -2
3 1 -2 -3 -2 1 3
12 13 4 -3 -8 -11 -6
12 -11 4 -3 -8 13 -6
----------------------  m = 13.  14 lattice points.
7 7
0 1 1 1 1 1 1
84 97 37 -11 -47 -71 -83
84 37 -47 -83 -71 -11 97
84 -11 -83 -47 97 37 -71
84 -47 -71 97 -11 -83 37
84 -71 -11 37 -83 97 -47
84 -83 97 -71 37 -47 -11
----------------------  m = 14.  32 lattice points.
8 8
1 2 2 2 2 2 2 1
2 -2 4 -2 4 -2 4 -1
49 26 -22 -46 -46 -22 26 49
49 -22 -46 26 26 -46 -22 49
49 -46 26 -22 -22 26 -46 49
98 118 52 -2 -44 -74 -92 -49
98 -2 -92 -74 52 118 -44 -49
98 -74 -44 118 -92 -2 52 -49
----------------------  m = 15.  20 lattice points.
8 8
0 1 1 1 1 1 1 1
1 -1 -1 3 -1 -1 3 -1
12 1 -11 -11 1 25 1 -11
12 -11 1 1 -11 25 -11 1
37 47 23 3 -13 -25 -33 -37
37 23 -13 -33 -37 -25 3 47
37 -13 -37 3 47 -25 -33 23
37 -37 47 -33 23 -25 3 -13
----------------------  m = 16.  54 lattice points.
9 9
1 2 2 2 2 2 2 2 1
1 -1 2 -1 2 -1 2 -1 1
4 -1 -4 -1 8 -1 -4 -1 4
16 11 -4 -13 -16 -13 -4 11 16
16 -13 -4 11 -16 11 -4 -13 16
64 83 44 11 -16 -37 -52 -61 -32
64 11 -52 -61 -16 83 44 -37 -32
64 -37 -52 83 -16 -61 44 11 -32
64 -61 44 -37 -16 11 -52 83 -32
----------------------  m = 17.  18 lattice points.
9 9
0 1 1 1 1 1 1 1 1
144 193 109 37 -23 -71 -107 -131 -143
144 109 -23 -107 -143 -131 -71 37 193
144 37 -107 -143 -71 109 193 -23 -131
144 -23 -143 -71 193 37 -131 -107 109
144 -71 -131 109 37 -143 -23 193 -107
144 -107 -71 193 -131 -23 109 -143 37
144 -131 37 -23 -107 193 -143 109 -71
144 -143 193 -131 109 -107 37 -71 -23
----------------------  m = 18.  44 lattice points.
10 10
1 2 2 2 2 2 2 2 2 1
2 -2 4 -2 4 -2 4 -2 4 -1
3 -2 -2 6 -2 -2 6 -2 -2 3
6 2 -4 -6 -4 2 12 2 -4 -3
27 22 -2 -18 -26 -26 -18 -2 22 27
27 -2 -26 -18 22 22 -18 -26 -2 27
27 -26 22 -18 -2 -2 -18 22 -26 27
54 74 44 18 -4 -22 -36 -46 -52 -27
54 -22 -52 18 44 -46 -36 74 -4 -27
54 -46 -4 18 -52 74 -36 -22 44 -27
----------------------  m = 19.  20 lattice points.
10 10
0 1 1 1 1 1 1 1 1 1
180 253 157 73 1 -59 -107 -143 -167 -179
180 157 1 -107 -167 -179 -143 -59 73 253
180 73 -107 -179 -143 1 253 157 -59 -167
180 1 -167 -143 73 253 -59 -179 -107 157
180 -59 -179 1 253 -107 -167 73 157 -143
180 -107 -143 253 -59 -167 157 1 -179 73
180 -143 -59 157 -179 73 1 -167 253 -107
180 -167 73 -59 -107 157 -179 253 -143 1
180 -179 253 -167 157 -143 73 -107 1 -59
----------------------  m = 20.  74 lattice points.
11 11
1 2 2 2 2 2 2 2 2 2 1
1 -1 2 -1 2 -1 2 -1 2 -1 1
4 -1 -4 -1 8 -1 -4 -1 8 -1 -2
25 2 -22 -22 2 50 2 -22 -22 2 25
25 -22 2 2 -22 50 -22 2 2 -22 25
25 23 2 -13 -22 -25 -22 -13 2 23 25
25 -13 -22 23 2 -25 2 23 -22 -13 25
100 143 92 47 8 -25 -52 -73 -88 -97 -50
100 47 -52 -97 -88 -25 92 143 8 -73 -50
100 -73 -52 143 -88 -25 92 -97 8 47 -50
100 -97 92 -73 8 -25 -52 47 -88 143 -50

----------------------  m = 24.  96 lattice points.
13 13
1 2 2 2 2 2 2 2 2 2 2 2 1
1 -1 2 -1 2 -1 2 -1 2 -1 2 -1 1
3 -2 -2 6 -2 -2 6 -2 -2 6 -2 -2 3
4 -1 -4 -1 8 -1 -4 -1 8 -1 -4 -1 4
3 1 -2 -3 -2 1 6 1 -2 -3 -2 1 3
16 11 -4 -13 -16 -13 -4 11 32 11 -4 -13 -8
16 -13 -4 11 -16 11 -4 -13 32 -13 -4 11 -8
12 13 4 -3 -8 -11 -12 -11 -8 -3 4 13 12
12 -11 4 -3 -8 13 -12 13 -8 -3 4 -11 12
48 73 52 33 16 1 -12 -23 -32 -39 -44 -47 -24
48 1 -44 -39 16 73 -12 -47 -32 33 52 -23 -24
48 -23 -44 33 16 -47 -12 73 -32 -39 52 1 -24
48 -47 52 -39 16 -23 -12 1 -32 33 -44 73 -24
----------------------  m = 28.  92 lattice points.
15 15
1 2 2 2 2 2 2 2 2 2 2 2 2 2 1
1 -1 2 -1 2 -1 2 -1 2 -1 2 -1 2 -1 1
4 -1 -4 -1 8 -1 -4 -1 8 -1 -4 -1 8 -1 -2
49 26 -22 -46 -46 -22 26 98 26 -22 -46 -46 -22 26 49
49 -22 -46 26 26 -46 -22 98 -22 -46 26 26 -46 -22 49
49 -46 26 -22 -22 26 -46 98 -46 26 -22 -22 26 -46 49
49 59 26 -1 -22 -37 -46 -49 -46 -37 -22 -1 26 59 49
49 -1 -46 -37 26 59 -22 -49 -22 59 26 -37 -46 -1 49
49 -37 -22 59 -46 -1 26 -49 26 -1 -46 59 -22 -37 49
196 311 236 167 104 47 -4 -49 -88 -121 -148 -169 -184 -193 -98
196 167 -4 -121 -184 -193 -148 -49 104 311 236 47 -88 -169 -98
196 47 -148 -193 -88 167 236 -49 -184 -169 -4 311 104 -121 -98
196 -121 -148 311 -88 -169 236 -49 -184 167 -4 -193 104 47 -98
196 -169 -4 47 -184 311 -148 -49 104 -193 236 -121 -88 167 -98
196 -193 236 -169 104 -121 -4 -49 -88 47 -148 167 -184 311 -98
----------------------  m = 32.  122 lattice points.
17 17
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1
1 -1 2 -1 2 -1 2 -1 2 -1 2 -1 2 -1 2 -1 1
4 -1 -4 -1 8 -1 -4 -1 8 -1 -4 -1 8 -1 -4 -1 4
16 11 -4 -13 -16 -13 -4 11 32 11 -4 -13 -16 -13 -4 11 16
16 -13 -4 11 -16 11 -4 -13 32 -13 -4 11 -16 11 -4 -13 16
64 83 44 11 -16 -37 -52 -61 -64 -61 -52 -37 -16 11 44 83 64
64 11 -52 -61 -16 83 44 -37 -64 -37 44 83 -16 -61 -52 11 64
64 -37 -52 83 -16 -61 44 11 -64 11 44 -61 -16 83 -52 -37 64
64 -61 44 -37 -16 11 -52 83 -64 83 -52 11 -16 -37 44 -61 64
256 419 332 251 176 107 44 -13 -64 -109 -148 -181 -208 -229 -244 -253 -128
256 251 44 -109 -208 -253 -244 -181 -64 107 332 419 176 -13 -148 -229 -128
256 107 -148 -253 -208 -13 332 251 -64 -229 -244 -109 176 419 44 -181 -128
256 -13 -244 -181 176 251 -148 -253 -64 419 44 -229 -208 107 332 -109 -128
256 -109 -244 107 176 -229 -148 419 -64 -253 44 251 -208 -181 332 -13 -128
256 -181 -148 419 -208 -109 332 -229 -64 251 -244 -13 176 -253 44 107 -128
256 -229 44 -13 -208 419 -244 107 -64 -181 332 -253 176 -109 -148 251 -128
256 -253 332 -229 176 -181 44 -109 -64 -13 -148 107 -208 251 -244 419 -128
----------------------  m = 36.  138 lattice points.
19 19
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1
1 -1 2 -1 2 -1 2 -1 2 -1 2 -1 2 -1 2 -1 2 -1 1
3 -2 -2 6 -2 -2 6 -2 -2 6 -2 -2 6 -2 -2 6 -2 -2 3
4 -1 -4 -1 8 -1 -4 -1 8 -1 -4 -1 8 -1 -4 -1 8 -1 -2
3 1 -2 -3 -2 1 6 1 -2 -3 -2 1 6 1 -2 -3 -2 1 3
27 22 -2 -18 -26 -26 -18 -2 22 54 22 -2 -18 -26 -26 -18 -2 22 27
27 -2 -26 -18 22 22 -18 -26 -2 54 -2 -26 -18 22 22 -18 -26 -2 27
27 -26 22 -18 -2 -2 -18 22 -26 54 -26 22 -18 -2 -2 -18 22 -26 27
12 13 4 -3 -8 -11 -12 -11 -8 -3 4 13 24 13 4 -3 -8 -11 -6
12 -11 4 -3 -8 13 -12 13 -8 -3 4 -11 24 -11 4 -3 -8 13 -6
27 37 22 9 -2 -11 -18 -23 -26 -27 -26 -23 -18 -11 -2 9 22 37 27
27 -11 -26 9 22 -23 -18 37 -2 -27 -2 37 -18 -23 22 9 -26 -11 27
27 -23 -2 9 -26 37 -18 -11 22 -27 22 -11 -18 37 -26 9 -2 -23 27
108 181 148 117 88 61 36 13 -8 -27 -44 -59 -72 -83 -92 -99 -104 -107 -54
108 61 -44 -99 -104 -59 36 181 88 -27 -92 -107 -72 13 148 117 -8 -83 -54
108 13 -92 -99 -8 181 36 -83 -104 -27 148 61 -72 -107 -44 117 88 -59 -54
108 -59 -92 117 -8 -107 36 61 -104 -27 148 -83 -72 181 -44 -99 88 13 -54
108 -83 -44 117 -104 13 36 -107 88 -27 -92 181 -72 -59 148 -99 -8 61 -54
108 -107 148 -99 88 -83 36 -59 -8 -27 -44 13 -72 61 -92 117 -104 181 -54
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