%I
%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 stereoisometric.
%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
