

A133159


A symmetrybreaking 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



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

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 nonEuclideantype asymmetrical displacement of a hexagonal close packed crystal unit cell.


LINKS



FORMULA

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}


MATHEMATICA

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]


CROSSREFS



KEYWORD

nonn,uned,obsc


AUTHOR



EXTENSIONS



STATUS

approved



