Acronym | ... |
Name | tri-hexagonal rhombic tiling |
Vertex figure | [r6], [R3] |
Dual | that |
Confer |
|
External links |
The rhombs can easily decomposed into pairs of regular triangles (therefore r=60°, R=120°). Then this tiling becomes just trat. – It also can be seen as the dual of that.
This tiling further could be considered as a vertex overlay of hexat plus 3 shifted copies of trats with edge size 3. Then this decomposition allows for a further 3-step partial Stott expansion running through rhomb-uBxx3xoAo3xooA3*a&#zx and rhomb-uBxx3uxBx3xooA3*a&#zx towards a pure hexat (A = 3x, B = 4x).Incidence matrix according to Dynkin symbol
(rhombic) xAoo3xoAo3xooA3*a&#zx (N → ∞, A = 3x) o...3o...3o...3*a | 6N * * * | 1 1 1 | 1 1 1 [R3] .o..3.o..3.o..3*a | * N * * | 6 0 0 | 0 3 3 [r6] ..o.3..o.3..o.3*a | * * N * | 0 6 0 | 3 0 3 [r6] ...o3...o3...o3*a | * * * N | 0 0 6 | 3 3 0 [r6] ----------------------+----------+----------+--------- oo..3oo..3oo..3*a&#x | 1 1 0 0 | 6N * * | 0 1 1 o.o.3o.o.3o.o.3*a&#x | 1 0 1 0 | * 6N * | 1 0 1 o..o3o..o3o..o3*a&#x | 1 0 0 1 | * * 6N | 1 1 0 ----------------------+----------+----------+--------- x.oo .... .... &#xt | 2 0 1 1 | 0 2 2 | 3N * * .... xo.o .... &#xt | 2 1 0 1 | 2 0 2 | * 3N * .... .... xoo. &#xt | 2 1 1 0 | 2 2 0 | * * 3N
or o...3o...3o...3*a | 2N * | 3 | 3 [R3] .o..3.o..3.o..3*a & | * N | 6 | 6 [r6] ------------------------+------+----+--- oo..3oo..3oo..3*a&#x & | 1 1 | 6N | 2 ------------------------+------+----+--- x.oo .... .... &#xt & | 2 2 | 4 | 3N
© 2004-2024 | top of page |