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%I #2 Mar 30 2012 17:34:22
%S 1,3,6,8,1,4,6,11,1,2,3,4,5,12,1,8,11,12,1,3,6,8,3,5,6,10,1,2,3,4,5,
%T 12,3,8,10,12,2,5,6,7,1,3,6,8,2,4,6,9,3,5,6,10,1,4,6,11,6,7,8,9,10,11,
%U 1,3,6,8,1,8,11,12,3,8,10,12,6,7,8,9,10,11,1,3,6,8,1,4,6,11,1,2,3,4,5,12,1
%N Two filled pentagons connected in a substitution graph in analogy to the hexagonal close pack A131213: the object is a 12 tone musical substitution. Characteristic polynomial: 12 + 120 x + 448 x^2 + 700 x^3 + 165 x^4 - 696 x^5 - 490 x^6 + 216 x^7 + 195 x^8 - 20 x^9 - 26 x^10 + x^12.
%C The relative geometry is 5 to 1: 5 quarters to one dime in relative sizes. The counter geometry is seven dimes to one quarter.
%F 1-> {2, 5, 6, 7};
%F 2-> {1, 3, 6, 8};
%F 3-> {2, 4, 6, 9};
%F 4-> {3, 5, 6, 10};
%F 5-> {1, 4, 6, 11};
%F 6-> {1, 2, 3, 4, 5, 12};
%F 7-> {1, 8, 11, 12};
%F 8-> {2, 7, 9, 12};
%F 9-> {3, 8,10, 12};
%F 10-> {4, 9, 11, 12};
%F 11-> {5, 7, 10, 12};
%F 12-> {6, 7, 8, 9, 10, 11};
%t Clear[s] s[1] = {2, 5, 6, 7}; s[2] = {1, 3, 6, 8}; s[3] = {2, 4, 6, 9}; s[4] = {3, 5, 6, 10}; s[5] = {1, 4, 6, 11}; s[6] = {1, 2, 3, 4, 5, 12}; s[7] = {1, 8, 11, 12}; s[8] = {2, 7, 9, 12}; s[9] = {3, 8,10, 12}; s[10] = {4, 9, 11, 12}; s[11] = {5, 7, 10, 12}; s[12] = {6, 7, 8, 9, 10, 11}; 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
%O 1,2
%A _Roger L. Bagula_, Oct 09 2007
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