Acronym ...
Name hyperbolic order 3 tritetragonal tiling
 
 ©   
Circumradius sqrt[-3 sqrt(2)/8] = 0.728238 i
Vertex figure [(3,4)3]
Confer
related hyperbolic polytopes:
pex-o3o4o3*a   pabex-o3o4o3*a   pac-o3o4x3*a  
general polytopal classes:
partial Stott expansions  
External
links
wikipedia  

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}

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