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 A133159 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. 1

%I #6 Mar 30 2012 17:34:22

%S 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,

%T 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,

%U 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

%N 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.

%C 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.

%F 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}

%t 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]

%Y Cf. A131213.

%K nonn,uned,obsc

%O 1,2

%A _Roger L. Bagula_, Oct 08 2007

%E Definition is not clear. - _N. J. A. Sloane_, May 06 2008

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Last modified October 3 10:37 EDT 2023. Contains 365861 sequences. (Running on oeis4.)