A105950 - OEIS

%I #4 Mar 30 2012 17:34:15

%S 1,1,2,3,4,5,9,1,2,3,4,5,9,2,3,4,5,9,1,3,4,6,10,1,2,4,7,11,1,2,3,8,12,

%T 6,7,8,1,9,10,11,12,1,5,1,2,3,4,5,9,2,3,4,5,9,1,3,4,6,10,1,2,4,7,11,1,

%U 2,3,8,12,6,7,8,1,9,10,11,12,1,5,2,3,4,5,9,1,3,4,6,10,1,2,4,7,11,1,2,3,8,12

%N 12 symbol hyper5tetrahedron : three tetrahedra with 5 connections per vertex: a triangle of tetrahedra connected.

%C This hyper5tetrahedron can be projected in 3d on an icosahedron. The characteristic polynomials has the roots: {{x -> -2.}, {x -> -2.}, {x -> -2.}, {x -> -2.}, {x -> -2.}, {x -> -2.}, { x -> 1.}, {x -> 1.}, {x -> 1.}, {x -> 2.}, {x -> 2.}, {x -> 5.}} which is in geometrical terms stereo-isometric.

%F 1->{2, 3, 4, 5, 9}, 2->{1, 3, 4, 6, 10}, 3->{1, 2, 4, 7, 11}, 4->{1, 2, 3, 8, 12}, 5->{6, 7, 8, 1, 9}, 6->{5, 7, 8, 2, 10}, 7->{5, 6, 8, 3, 11}, 8->{5, 6, 7, 4, 12}, 9->{10, 11, 12, 1, 5}, 10->{9, 11, 12, 2, 6}, 11->{9, 10, 12, 3, 7}, 12->{9, 10, 11, 4, 8}

%t s[1] = {2, 3, 4, 5, 9}; s[2] = {1, 3, 4, 6, 10}; s[3] = {1, 2, 4, 7, 11}; s[4] = {1, 2, 3, 8, 12}; s[5] = {6, 7, 8, 1, 9}; s[6] = {5, 7, 8, 2, 10}; s[7] = {5, 6, 8, 3, 11}; s[8] = {5, 6, 7, 4, 12}; s[9] = {10, 11, 12, 1, 5}; s[10] = {9, 11, 12, 2, 6}; s[11] = {9, 10, 12, 3, 7}; s[12] = {9, 10, 11, 4, 8}; t[a_] := Join[a, Flatten[s /@ a]]; p[0] = {1}; p[1] = t[{1}]; p[n_] := t[p[n - 1]] a = Flatten[Table[p[n], {n, 0, 3}]]

%K nonn,uned

%O 0,3

%A _Roger L. Bagula_, Apr 27 2005