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A133159
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A symmetry-breaking on the graph substitution for hexagonal close packing (A131213) from two hexagons to a pentagon and heptagon while keeping the number of vertices constant: Characteristic polynomial is: 8 - 36 x - 332 x^2 + 314 x^3 + 3833 x^4 + 5492 x^5 + 584 x^6 - 3196 x^7 - 1315 x^8 + 596 x^9 + 354 x^10 - 36 x^11 - 34 x^12 + x^14.
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1
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1, 3, 6, 8, 9, 1, 4, 6, 12, 13, 1, 2, 3, 4, 5, 1, 8, 13, 14, 1, 3, 6, 8, 9, 3, 5, 6, 11, 12, 2, 3, 8, 10, 14, 3, 9, 11, 14, 2, 5, 6, 7, 1, 3, 6, 8, 9, 2, 4, 9, 10, 3, 5, 6, 11, 12, 1, 4, 6, 12, 13, 1, 3, 6, 8, 9, 1, 8, 13, 14, 2, 3, 8, 10, 14, 6, 7, 8, 9, 10, 11, 12, 13, 1, 3, 6, 8, 9, 2, 4, 9, 10, 2, 7
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refs;
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OFFSET
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1,2
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COMMENTS
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The idea here is a displaced packing of spheres that is like the 7 tone (naturals) to 5 tone (flats) scale of 12 tone music. In geometrical terms it would be a non-Euclidean-type asymmetrical displacement of a hexagonal close packed crystal unit cell.
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LINKS
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FORMULA
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1->{2, 5, 6, 7}; 2->{1, 3, 6, 8, 9}; 3->{2, 4, 9, 10}; 4->{3, 5, 6, 11, 12}; 5->{1, 4, 6, 12, 13}; 6->{1, 2, 3, 4, 5}; 7->{1, 8, 13, 14}; 8->{2,7, 9, 14}; 9->{2, 3, 8, 10, 14}; 10->{3, 9, 11, 14}; 11->{4, 10, 12, 14}; 12->{4, 5, 11, 13, 14}; 13->{5, 7, 11, 14}; 14->{6,7, 8, 9, 10, 11, 12, 13}
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MATHEMATICA
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Clear[s] s[1] = {2, 5, 6, 7}; s[2] = {1, 3, 6, 8, 9}; s[3] = {2, 4, 9, 10}; s[4] = {3, 5, 6, 11, 12}; s[5] = {1, 4, 6, 12, 13}; s[6] = {1, 2, 3, 4, 5}; s[7] = {1, 8, 13, 14}; s[8] = {2, 7, 9, 14}; s[9] = {2, 3, 8, 10, 14}; s[10] = {3, 9, 11, 14}; s[11] = { 4, 10, 12, 14}; s[12] = {4, 5, 11, 13, 14}; s[13] = {5, 7, 11, 14}; s[14] = {6, 7, 8, 9, 10, 11, 12, 13}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]]; aa = p[4]
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CROSSREFS
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KEYWORD
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nonn,uned,obsc
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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