Acronym | ... |
Name | uBxx3xoAo3xooA3*a&#zx |
Vertex figure | [36], [34,6], [(3,6)2] |
Confer |
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Trat could be considered as a vertex overlay of hexat plus 3 shifted copies of trats with edge size 3 (see there). This decomposition allows for a 3-step transformation running then through this tiling and uBxx3uxBx3xooA3*a&#zx towards a pure hexat (A = 3x, B = 4x). – So this transformation sequence is not a true partial Stott expansion one because pairs of triangles become transformed into single hexagons. But this could be recovered by combining these pairs into rhombs. The corresponding sequence member here then would be rhomb-uBxx3xoAo3xooA3*a&#zx.
Incidence matrix according to Dynkin symbol
uBxx3xoAo3xooA3*a&#zx (N → ∞, A = 3x, B = 4x) o...3o...3o...3*a | 6N * * * | 1 1 1 1 1 0 0 | 1 1 1 1 1 0 0 [34,6] .o..3.o..3.o..3*a | * N * * | 0 0 6 0 0 0 0 | 3 3 0 0 0 0 0 [36] ..o.3..o.3..o.3*a | * * 3N * | 0 0 0 2 0 2 0 | 0 0 1 0 2 1 0 [(3,6)2] ...o3...o3...o3*a | * * * 3N | 0 0 0 0 2 0 2 | 0 0 0 1 2 0 1 [(3,6)2] ----------------------+------------+----------------------+------------------- .... x... .... | 2 0 0 0 | 3N * * * * * * | 1 0 0 1 0 0 0 .... .... x... | 2 0 0 0 | * 3N * * * * * | 0 1 1 0 0 0 0 oo..3oo..3oo..3*a | 1 1 0 0 | * * 6N * * * * | 1 1 0 0 0 0 0 o.o.3o.o.3o.o.3*a | 1 0 1 0 | * * * 6N * * * | 0 0 1 0 1 0 0 o..o3o..o3o..o3*a | 1 0 0 1 | * * * * 6N * * | 0 0 0 1 1 0 0 ..x. .... .... | 0 0 2 0 | * * * * * 3N * | 0 0 0 0 1 1 0 ...x .... .... | 0 0 0 2 | * * * * * * 3N | 0 0 0 0 1 0 1 ----------------------+------------+----------------------+------------------- .... xo.. .... &#x | 2 1 0 0 | 1 0 2 0 0 0 0 | 3N * * * * * * .... .... xo.. &#x | 2 1 0 0 | 0 1 2 0 0 0 0 | * 3N * * * * * .... .... x.o. &#x | 2 0 1 0 | 0 1 0 2 0 0 0 | * * 3N * * * * .... x..o .... &#x | 2 0 0 1 | 1 0 0 0 2 0 0 | * * * 3N * * * u.xx .... .... &#xt | 2 0 2 2 | 0 0 0 2 2 1 1 | * * * * 3N * * ..x. .... ..o.3*a | 0 0 3 0 | 0 0 0 0 0 3 0 | * * * * * N * ...x3...o .... | 0 0 0 3 | 0 0 0 0 0 0 3 | * * * * * * N
or o...3o...3o...3*a | 6N * * | 2 1 2 0 | 2 2 1 0 [34,6] .o..3.o..3.o..3*a | * N * | 0 6 0 0 | 6 0 0 0 [36] ..o.3..o.3..o.3*a & | * * 6N | 0 0 2 2 | 0 1 2 1 [(3,6)2] ------------------------+---------+--------------+------------ .... x... .... & | 2 0 0 | 6N * * * | 1 1 0 0 oo..3oo..3oo..3*a | 1 1 0 | * 6N * * | 2 0 0 0 o.o.3o.o.3o.o.3*a & | 1 0 1 | * * 12N * | 0 1 1 0 ..x. .... .... & | 0 0 2 | * * * 6N | 0 0 1 1 ------------------------+---------+--------------+------------ .... xo.. .... &#x & | 2 1 0 | 1 2 0 0 | 6N * * * .... .... x.o. &#x & | 2 0 1 | 1 0 2 0 | * 6N * * u.xx .... .... &#xt | 2 0 4 | 0 0 4 2 | * * 3N * ..x. .... ..o.3*a & | 0 0 3 | 0 0 0 3 | * * * 2N
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