| Acronym | ditetsquat (old: dittitecat) |
| Name |
hyperbolic order 3 tritetragonal tiling, hyperbolic ditrigonary triangle-square tiling, hyperbolic ditrigonary tritetragonal tiling, hyperbolic alternated octagonal tiling |
| |
| Circumradius | sqrt[-3 sqrt(2)/8] = 0.728238 i |
| Vertex figure | [(3,4)3] |
| Confer |
|
|
External links |
|
This tiling allows for a consistent 4-coloring of the triangles. This then could give rise for a series of partial Stott contractions, each reducing one set of triangles piecewise into points.
Incidence matrix according to Dynkin symbol
x3o3o4*a (N → ∞) . . . | 4N | 6 | 3 3 ---------+----+-----+------ x . . | 2 | 12N | 1 1 ---------+----+-----+------ x3o . | 3 | 3 | 4N * x . o4*a | 4 | 4 | * 3N
o3o8s (N → ∞)
demi( . . . ) | 4N | 6 | 3 3
--------------+----+-----+------
sefa( . o8s ) | 2 | 12N | 1 1
--------------+----+-----+------
. o8s ♦ 4 | 4 | 3N *
sefa( o3o8s ) | 3 | 3 | * 4N
starting figure: o3o8x
s4s8o (N → ∞)
demi( . . . ) | 4N | 4 2 | 2 1 3
--------------+----+-------+--------
sefa( s4s . ) | 2 | 8N * | 1 0 1
sefa( . s8o ) | 2 | * 4N | 0 1 1
--------------+----+-------+--------
s4s . ♦ 4 | 4 0 | 2N * *
. s8o ♦ 4 | 0 4 | * N *
sefa( s4s8o ) | 3 | 2 1 | * * 4N
starting figure: x4x8o
s4s4s4*a (N → ∞)
demi( . . . ) | 4N | 2 2 2 | 1 1 1 3
-----------------+----+----------+---------
sefa( s4s . ) | 2 | 4N * * | 1 0 0 1
sefa( s . s4*a ) | 2 | * 4N * | 0 1 0 1
sefa( . s4s ) | 2 | * * 4N | 0 0 1 1
-----------------+----+----------+---------
s4s . ♦ 4 | 4 0 0 | N * * *
s . s4*a ♦ 4 | 0 4 0 | * N * *
. s4s ♦ 4 | 0 0 4 | * * N *
sefa( s4s4s4*a ) | 3 | 1 1 1 | * * * 4N
starting figure: x4x4x4*a
acc. to 4-coloring of triangles: y,b,s,g (N → ∞)
2N * * * | 1 1 0 1 1 0 1 1 0 0 0 0 | 1 1 1 0 1 1 0 1 0 0 ybs [(3,4)^3]
* 2N * * | 1 0 1 1 0 1 0 0 0 1 1 0 | 1 1 0 1 1 0 1 0 1 0 ybg [(3,4)^3]
* * 2N * | 0 1 1 0 0 0 1 0 1 1 0 1 | 1 0 1 1 0 1 1 0 0 1 ysg [(3,4)^3]
* * * 2N | 0 0 0 0 1 1 0 1 1 0 1 1 | 0 1 1 1 0 0 0 1 1 1 bsg [(3,4)^3]
------------+-------------------------------------+------------------------
1 1 0 0 | 2N * * * * * * * * * * * | 1 0 0 0 1 0 0 0 0 0 y:b:sg
1 0 1 0 | * 2N * * * * * * * * * * | 1 0 0 0 0 1 0 0 0 0 y:s:bg
0 1 1 0 | * * 2N * * * * * * * * * | 1 0 0 0 0 0 1 0 0 0 y:g:bs
1 1 0 0 | * * * 2N * * * * * * * * | 0 1 0 0 1 0 0 0 0 0 b:y:sg
1 0 0 1 | * * * * 2N * * * * * * * | 0 1 0 0 0 0 0 1 0 0 b:s:yg
0 1 0 1 | * * * * * 2N * * * * * * | 0 1 0 0 0 0 0 0 1 0 b:g:ys
1 0 1 0 | * * * * * * 2N * * * * * | 0 0 1 0 0 1 0 0 0 0 s:y:bg
1 0 0 1 | * * * * * * * 2N * * * * | 0 0 1 0 0 0 0 1 0 0 s:b:yg
0 0 1 1 | * * * * * * * * 2N * * * | 0 0 1 0 0 0 0 0 0 1 s:g:yb
0 1 1 0 | * * * * * * * * * 2N * * | 0 0 0 1 0 0 1 0 0 0 g:y:bs
0 1 0 1 | * * * * * * * * * * 2N * | 0 0 0 1 0 0 0 0 1 0 g:b:ys
0 0 1 1 | * * * * * * * * * * * 2N | 0 0 0 1 0 0 0 0 0 1 g:s:yb
------------+-------------------------------------+------------------------
1 1 1 0 | 1 1 1 0 0 0 0 0 0 0 0 0 | 2N * * * * * * * * * y {3}
1 1 0 1 | 0 0 0 1 1 1 0 0 0 0 0 0 | * 2N * * * * * * * * b {3}
1 0 1 1 | 0 0 0 0 0 0 1 1 1 0 0 0 | * * 2N * * * * * * * s {3}
0 1 1 1 | 0 0 0 0 0 0 0 0 0 1 1 1 | * * * 2N * * * * * * g {3}
2 2 0 0 | 2 0 0 2 0 0 0 0 0 0 0 0 | * * * * N * * * * * yb {4}
2 0 2 0 | 0 2 0 0 0 0 2 0 0 0 0 0 | * * * * * N * * * * ys {4}
0 2 2 0 | 0 0 2 0 0 0 0 0 0 2 0 0 | * * * * * * N * * * yg {4}
2 0 0 2 | 0 0 0 0 2 0 0 2 0 0 0 0 | * * * * * * * N * * bs {4}
0 2 0 2 | 0 0 0 0 0 2 0 0 0 0 2 0 | * * * * * * * * N * bg {4}
0 0 2 2 | 0 0 0 0 0 0 0 0 2 0 0 2 | * * * * * * * * * N sg {4}
© 2004-2024 | top of page |