

A105950


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


0



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
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OFFSET

0,3


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 stereoisometric.


LINKS

Table of n, a(n) for n=0..98.


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}


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}]]


CROSSREFS

Sequence in context: A079383 A103670 A289081 * A227778 A166276 A101544
Adjacent sequences: A105947 A105948 A105949 * A105951 A105952 A105953


KEYWORD

nonn,uned


AUTHOR

Roger L. Bagula, Apr 27 2005


STATUS

approved



