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A105950
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12 symbol hyper5tetrahedron : three tetrahedra with 5 connections per vertex: a triangle of tetrahedra connected.
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0
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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, 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, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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.
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FORMULA
| 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}
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MATHEMATICA
| 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}]]
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CROSSREFS
| Sequence in context: A057657 A079383 A103670 * A166276 A101544 A171100
Adjacent sequences: A105947 A105948 A105949 * A105951 A105952 A105953
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 27 2005
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