An Alternate View of Nuclear Structure

Solutions Derived from S001L6

Aran David Stubbs



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Summary

Solution Main

These are solution points derived from a primary solution linked above. These typically have some dipole when all the surface monoquarks are ups, so a calculation is needed to find how many surface monoquarks should become downs to minimize dipole. Dipole can occur in any of the 7 axises defined for an octahedra, but only the x, y, z, and ++ axis are relevant (since there can only be significant dipole on an axis perpendicular to 2 faces when the solution is diagonalized). The z axis is the long axis in the base case, assigned arbitrarily when all 3 are the same length. X is the intermediate length axis, and y is the shortest axis.

Derivations: x is the extended form (if any), s is a sphere, t a triangle (number following is the number of spheres along an edge), h is a hexagon (h2 has 7 spheres, h3 12, h4 18, etc.). The number preceding a symbol is the count of that symbol added. Additions are made so as to minimize the addition to dipole. Dipole formula is the count of the dominant type in a hemisphere plus the subordinate type if the axis is even in length, or dominant plus subordinate plus half the equator length if the axis is odd. Maximum z occurs when the dominant type is treated as dipole and the subordinate type as up monoquarks, total charge is twice the charge on the dipole dominated hemisphere (rounded up to the nearest integer). Link (if any) connects to a Sketchup of the solution.


A Derivation   Surface   Dipole
Formula  		 Axis   Max
Z 		Min
SD 		Link  
263 -18s 97 49+48 z 97 0 Link
265 -14s 97 49+48 z 97 0 Link
267 -10s 97 49+48 z 97 0 Link
268 -8s 97 50+47 z 96 1 Link
269 -6s 97 51+46 z 96 1 Link
270 -4s 97 52+45 z 95 2 Link
271 -2s 97 53+44 z 94 3 Link
272 ... 97 54+43 z 94 3 Link
273 x (+2s vertex) 97 55+42 z 93 4 Link
273 +2s face 98 54+44 z 95 3
274 x+2s 98 55+43 z 94 4
275 x+4s 99 55+44 z 96 3 Link
275 +2t2 99 55+44 z 96 3 Link
276 x+2t2 99 54+45 z 96 3
277 x+2t2+2s 100 54+46 z 98 2
278 x+2t2+4s 101 54+47 z 99 2
279 x+2t3 100 51+42+14/2 y 97 3
279 x+4t2 101 53+48 z 100 1
280 x+2t3+2s 101 51+43+14/2 y 99 2
280 x+2h2 101 52+42+14/2 y 98 3
280 x+4t2+2s 102 53+49 z 101 1
281 x+2t4-4s 101 53+41+14/2 y 97 4
281 x+2t3+4s 102 51+44+14/2 y 100 2
281 x+2h2+2s 102 52+43+14/2 y 99 3
281 x+4t2+4s 103 53+50 z 102 1
282 x+2t4-2s 101 54+40+14/2 y 97 4
282 x+2t3+2t2 102 50+45+14/2 y 101 1
282 x+(2t4-4s)+2s 102 53+42+14/2 y 99 3
282 +4t3-4s 103 52+51 z 103 0
282 x+2h2+4s 103 52+44+14/2 y 101 2
283 x+2t4 101 55+39+14/2 y 96 5
283 x+(2t4-2s)+2s 102 54+41+14/2 y 98 4
283 x+4t3-4s 103 52+51 z 103 0
283 x+2t3+2t2+2s 103 50+46+14/2 y 102 1
283 x+2h2+2t2 103 51+45+14/2 y 101 2
283 x+(2t4-4s)+4s 103 53+43+14/2 y 100 3
284 x+2t4+2s 102 55+40+14/2 y 97 5
284 +4t3 103 53+50 z 102 1
284 x+(2t4-4s)+2t2 103 52+44+14/2 y 101 2
284 x+(2t4-2s)+4s 103 54+42+14/2 y 98 5
284 x+2h2+2t2+2s 104 51+46+14/2
53+51		 y
z		 103
104		 1
0
285 x+2h3 102 57+38+14/2 y 96 6
285 x+4t3 103 54+49 z 102 1
285 x+(2t4-2s)+2t2 103 53+43+14/2 y 100 3
285 x+2t4+4s 103 55+41+14/2 y 99 4
285 +4t3+2s 104 53+51 z 104 0
285 x+2h2+(2t3-2s) 104 50+47+14/2
54+50		 y
z		 103 1
285 x+(2t4-4s)+2t2+2s 104 52+45+14/2 y 102 2
286 x+2h3+2s 103 57+39+14/2 y 97 6
286 x+2t4+2t2 103 54+42+14/2 y 99 4
286 x+4t3+2s 104 54+50 z 103 1
286 x+2h2+2t3 104 55+49 z 102 2
286 x+(2t4-4s)+(2t3-2s) 104 51+46+14/2
55+49		 y
z		 102 2
286 x+(2t4-2s)+2t2+2s 104 53+44+14/2 y 100 4
286 +4t3+4s 105 53+52 z 105 0
287 x+(2t4-2s)+(2t3-2s) 104 52+45+14/2
56+48		 y
z		 101
102		 3
287 x+2h3+4s 104 57+40+14/2 y 99 5
287 x+(2t4-4s)+2t3 104 56+48 z 102 2
287 x+2t4+2t2+2s 104 54+43+14/2
56+48		 y
z		 101
102		 3
2
287 x+4t3+4s 105 54+51 z 104 1
287 x+4h2 105 56+49 z 103 2
288 x+2h3+2t2 104 56+41+14/2
57+47		 y
z		 99
101		 3
5
288 x+(2t4-2s)+2t3 104 57+47 z 101 3
288 x+2t4+(2t3-2s) 104 53+44+14/2
57+47		 y
z		 101 3
288 x+4t3+2t2 105 53+52
50+46+18/2		 z
x		 105
104		 0
1
288 x+(2t4-4s)+2t3+2s 105 56+49 z 103 2
288 x+(2t4-4s)+2h2 105 57+48 z 102 3
288 x+4h2+2s 106 56+50 z 104 2
289 x+2h3+2t2+2s 105 56+42+14/2
58+47		 y
z		 101
102		 4
3
289 x+2t4+2t3 104 58+46 z 100 4
289 x+4t4-8s 105 58+47 z 102 3
289 x+(2t4-2s)+2h2 105 58+47 z 102 3
289 x+(2t4-4s)+2h2+2s 106 57+49 z 104 2
289 x+4t3+2t2+2s 106 53+53
50+47+18/2		 z
x		 106
105		 0
1
289 x+4h2+4s 107 56+51 z 106 1
290 x+2h3+(2t3-2s) 105 55+43+14/2
59+46		 y
z		 101 4
290 x+4t4-6s 105 59+46 z 101 4
290 x+2t4+2h2 105 59+46 z 101 4
290 x+(4t4-8s)+2s 106 58+48 z 103 3
290 x+4t3+2t2+4s 107 54+53
50+48+18/2		 z
x		 107 0
290 x+(2t4-4s)+2h2+4s 107 57+50 z 105 2
290 x+4h2+2t2 107 55+52
51+47+18/2		 z
x		 106 1
291 x+4t4-4s 105 60+45 z 100 5
291 x+2h3+2t3 105 54+44+14/2
60+45		 y
z		 102
100		 3
5
291 x+(4t4-6s)+2s 106 59+47 z 102 4
291 x+4t3+4t2 107 55+52 z 106 1
291 x+(2t4-4s)+2h2+2t2 107 56+51
51+47+18/2		 z
x		 106 1
291 x+(4t4-8s)+4s 107 58+49 z 104 3
291 x+4h2+2t2+2s 108 54+54
51+48+18/2		 z
x		 108
107		 0
1
292 x+4t4-2s 105 61+44 z 100 5
292 x+(4t4-4s)+2s 106 60+46 z 102 4
292 x+2h3+2t3+2s 106 54+45+14/2
61+45		 y
z		 103
101		 3
5
292 x+2h3+2h2 106 54+45+14/2
61+45		 y
z		 103
101		 3
5
292 x+(4t4-8s)+2t2 107 57+50
51+47+18/2		 z
x		 105
106		 2
1
292 x+(4t4-6s)+4s 107 59+48 z 104 3
292 x+(2t4-4s)+2h2+2t2+2s 108 56+52
51+48+18/2		 z
x		 107 1
292 x+4h2+(2t3-2s) 108 54+54
53+46+18/2		 z
x		 108
106		 0
2
292 x+4h2+2t2+4s 109 55+54
51+49+18/2		 z
x		 109 0
293 x+4t4 105 62+43 z 99 6
293 x+(4t4-2s)+2s 106 61+45 z 101 5
293 x+2h3+(2t4-4s) 106 53+46+14/2
62+44		 y
z		 104
100		 2
6
293 x+(4t4-6s)+2t2 107 58+49
51+47+18/2		 z
x		 104
106		 3
1
293 x+(4t4-4s)+4s 107 60+47 z 103 4
293 x+4h2+2t3 108 55+53
54+45+18/2		 z
x		 108
105		 0
3
293 x+(4t4-8s)+2t2+2s 108 57+51
51+48+18/2		 z
x		 106
107		 2
1
293 x+(2t4-4s)+2h2+(2t3-2s) 108 55+53
53+46+18/2		 z
x		 108
106
 0
2
293 x+4h2+4t2 109 56+53
50+50+18/2		 z
x		 108
109		 1
0
293 x+(2t4-4s)+2h2+2t2+4s 109 56+53
51+49+18/2		 z
x		 108
109		 1
0
293 x+4h2+(2t3-2s)+2s 109 55+54
53+47+18/2		 z
x		 109
107		 0
2
294 x+4t4+2s 106 62+44 z 100 6
294 x+2h3+(2t4-2s) 106 52+47+14/2
63+43		 y
z		 105
100		 1
6
294 x+(4t4-4s)+2t2 107 59+48
51+47+18/2		 z
x		 104
106		 3
1
294 x+(4t4-2s)+4s 107 61+46 z 102 5
294 x+(4t4-8s)+(2t3-2s) 108 55+53
53+46+18/2		 z
x		 108
106		 0
2
294 x+(4t4-6s)+2t2+2s 108 58+50
51+48+18/2		 z
x		 106
107		 2
1
294 x+(2t4-4s)+2h2+2t3 108 54+54
54+45+18/2		 z
x		 108
105
 0
3
294 x+4h2+2t3+2s 109 56+53
54+46+18/2		 z
x		 108
107		 1
2
294 x+(4t4-8s)+2t2+4s 109 57+52
51+49+18/2		 z
x		 108
109		 1
0
294 x+(2t4-4s)+2h2+4t2 109 55+54
52+50+14/2
50+50+18/2		 z
y
x		 109 0
294 x+(2t4-4s)+2h2+(2t3-2s)+2s 109 55+54
53+47+18/2		 z
x		 109
107
 0
2
294 x+4h2+(2t3-2s)+4s 110 56+54
53+48+18/2		 z
x		 110
109		 0
1
295 x+2h3+2t4 106 51+48+14/2
64+42		 y
z		 105
99		 1
7
295 x+(4t4-2s)+2t2 107 60+47
51+47+18/2		 z
x		 103
106		 4
1
295 x+4t4+4s 107 62+45 z 102 5
295 x+(4t4-4s)+2t2+2s 108 59+49
51+48+18/2		 z
x		 105
107		 3
1
295 x+(4t4-8s)+2t3 108 54+54
54+45+18/2		 z
x		 108
105		 0
3
295 x+(2t4-4s)+2h2+2t3+2s 109 55+54
54+46+18/2		 z
x		 109
107
 0
2
295 x+(4t4-8s)+4t2 109 56+53
50+50+18/2		 z
x		 108
109		 1
0
295 x+(4t4-6s)+2t2+4s 109 58+51
51+49+18/2		 z
x		 107
109		 2
0
295 x+(4t4-8s)+(2t3-2s)+2s 109 55+54
53+47+18/2		 z
x		 109
107		 0
2
295 x+4h2+(2t3-2s)+2t2 110 57+53
52+49+18/2		 z
x		 109 1
295 x+4h2+2t3+4s 110 57+53
54+47+18/2		 z
x		 109
108		 1
2
295 x+(2t4-4s)+2h2+(2t3-2s)+4s 110 55+55
52+49+18/2		 z
x		 110
109
 0
1
296 x+4t4+2t2 107 61+46 z 102 5
296 x+2h3+2t4+2s 107 51+49+14/2
64+43		 y
z		 107
100		 0
7
296 x+(4t4-6s)+2t3 108 56+52
54+45+18/2		 z
x		 107
105		 1
3
296 x+(4t4-4s)+(2t3-2s) 108 58+50
53+46+18/2		 z
x		 106 2
296 x+(4t4-2s)+2t2+2s 108 60+48
51+48+18/2		 z
x		 104
107		 4
1
296 x+(4t4-6s)+4t2 109 57+52
50+50+18/2		 z
x		 108
109		 1
0
296 x+(4t4-6s)+(2t3-2s)+2s 109 57+52
53+47+18/2		 z
x		 108
107		 1
2
296 x+(4t4-8s)+2t3+2s 109 55+54
54+46+18/2		 z
x		 109
107		 0
2
296 x+(4t4-4s)+2t2+4s 109 59+50
51+49+18/2		 z
x		 106
109		 3
0
296 x+(4t4-8s)+(2t3-2s)+4s 110 55+55
52+49+18/2		 z
x		 110
109		 0
1
296 x+(2t4-4s)+2h2+(2t3-2s)+2t2 110 56+54
52+49+18/2		 z
x		 109 1
297 x+(4t4-8s)+(2t3-2s)+2t2 110 56+54
52+49+18/2		 z
x		 109 1
296 x+(2t4-4s)+2h2+2t3+4s 110 56+54
54+47+18/2		 z
x		 110
108
 0
2
296 x+4h2+2t3+2t2 110 58+52
53+48+18/2		 z
x		 108
109		 2
1
297 x+4h3 107 66+41 z 99 8
297 x+(4t4-4s)+2t3 108 57+51
54+45+18/2		 z
x		 106
105		 2
3
297 x+(4t4-2s)+(2t3-2s) 108 59+49
53+46+18/2		 z
x		 105
106		 3
2
297 x+4t4+2t2+2s 108 61+47 z 104 4
297 x+2h3+2t4+4s 108 51+50+14/2
64+44		 y
z		 108
102		 0
6
297 x+(4t4-4s)+4t2 109 58+51
50+50+18/2		 z
x		 107
109		 2
0
297 x+(4t4-4s)+(2t3-2s)+2s 109 58+51
53+47+18/2		 z
x		 107 2
297 x+(4t4-6s)+2t3+2s 109 56+53
54+46+18/2		 z
x		 108
107		 1
2
297 x+(4t4-2s)+2t2+4s 109 60+49
51+49+18/2		 z
x		 106
109		 3
0
297 x+(4t4-6s)+(2t3-2s)+2t2 110 56+54
52+49+18/2		 z
x		 110
109		 0
1
297 x+(4t4-6s)+(2t3-2s)+4s 110 57+53
53+48+18/2		 z
x		 109 1
297 x+(2t4-4s)+2h2+2t3+2t2 110 57+53
53+48+18/2		 z
x		 109 1
297 x+(4t4-8s)+2t3+4s 110 56+54
54+47+18/2		 z
x		 110
108		 0
2
297 x+4h2+4t3-4s 111 59+52
51+51+18/2		 z
x		 109
111		 2
0
298 x+2t5-4s+2h3 107 67+40 z 98 9
298 x+(4t4-2s)+2t3 108 58+50
54+45+18/2		 z
x		 106
105		 2
3
298 x+4t4+(2t3-2s) 108 60+48
53+46+18/2		 z
x		 104
106		 4
2
298 x+(4t4-4s)+2t3+2s 109 57+52
54+46+18/2		 z
x		 108
107		 1
2
298 x+(4t4-2s)+4t2 109 59+50
50+50+18/2		 z
x		 106
109		 3
0
298 x+(4t4-2s)+(2t3-2s)+2s 109 59+50
53+47+18/2		 z
x		 106
107		 1
2
298 x+4t4+2t2+4s 109 61+48 z 105 4
298 x+(4t4-8s)+2t3+2t2 110 57+53
53+48+18/2		 z
x		 109 1
298 x+(4t4-4s)+(2t3-2s)+4s 110 58+52
53+48+18/2		 z
x		 108
109		 2
1
298 x+(4t4-6s)+2t3+4s 110 56+54
54+47+18/2		 z
x		 110
108		 0
2
298 x+(2t4-4s)+2h2+4t3-4s 111 58+53
51+51+18/2		 z
x		 110
111		 1
0
298 x+4h2+4t3-2s 111 60+51 z 108 3
299 x+4t5-8s 107 68+39 z 98 9
299 x+4t4+2t3 108 59+49
54+45+18/2		 z
x		 105 3
299 x+(4t4-2s)+2t3+2s 109 58+51
54+46+18/2		 z
x		 107 2
299 x+4t4+4t2 109 60+49 z 106 3
299 x+4t4+(2t3-2s)+2s 109 60+49
53+47+18/2		 z
x		 106
107		 3
2
299 x+(4t4-4s)+(2t3-2s)+2t2 110 57+53
52+49+18/2		 z
x		 109 1
299 x+(4t4-6s)+2t3+2t2 110 55+55
53+48+18/2		 z
x		 110
109		 0
1
299 x+(4t4-4s)+2t3+4s 110 57+53
54+47+18/2		 z
x		 109
108		 1
2
299 x+(4t4-2s)+(2t3-2s)+4s 110 59+51
53+48+18/2		 z
x		 108
109		 2
1
299 x+(4t4-8s)+4t3-4s 111 57+54 z 110 1
299 x+(2t4-4s)+2h2+4t3-2s 111 59+52 z 109 2
299 x+4h2+4t3 111 61+50 z 108 3
300 x+4t5-6s 107 69+38 z 97 10
300 x+4t4+2t3+2s 109 59+50
54+46+18/2		 z
x		 106
107		 3
2
300 x+(4t4-4s)+2t3+2t2 110 56+54
53+48+18/2		 z
x		 110
109		 0
1
300 x+(4t4-2s)+(2t3-2s)+2t2 110 58+52
52+49+18/2		 z
x		 108
109		 2
1
300 x+(4t4-2s)+2t3+4s 110 58+52
54+47+18/2		 z
x		 108 2
300 x+4t4+(2t3-2s)+4s 110 60+50
53+48+18/2		 z
x		 107
109		 3
1
300 x+(4t4-6s)+4t3-4s 111 56+55 z 111 0
300 x+(4t4-8s)+4t3-2s 111 58+53 z 110 1
300 x+(2t4-4s)+2h2+4t3 111 60+51 z 108 3
301 x+4t5-4s 107 70+37 z 96 11
301 x+(4t4-2s)+2t3+2t2 110 57+53
53+48+18/2		 z
x		 109 1
301 x+4t4+2t3+4s 110 59+51
54+47+18/2		 z
x		 108 2
301 x+4t4+(2t3-2s)+2t2 110 59+51
52+49+18/2		 z
x		 108
109		 2
1
301 x+(4t4-4s)+4t3-4s 111 56+55 z 111 0
301 x+(4t4-6s)+4t3-2s 111 57+54 z 110 1
301 x+(4t4-8s)+4t3 111 59+52 z
x		 109 2
302 x+4t5-2s 107 71+36 z 96 11
302 x+4t4+2t3+2t2 110 58+52
53+48+18/2		 z
x		 108
109		 2
1
302 x+(4t4-4s)+4t3-2s 111 56+55 z 111 0
302 x+(4t4-2s)+4t3-4s 111 57+54 z 110 1
302 x+(4t4-6s)+4t3 111 58+53 z 110 1
303 x+4t5 107 72+35 z 95 12
303 x+(4t4-2s)+4t3-2s 111 56+55 z 111 0
303 x+(4t4-4s)+4t3 111 57+54 z 110 1
303 x+4t4+4t3-4s 111 58+53 z 110 1
304 x+(4t4-2s)+4t3 111 56+55 z 111 0
304 x+4t4+4t3-2s 111 57+54 z 110 1
305 x+4t4+4t3 111 56+55 z 111 0