Acronym rothat
Name rhombitrihexagonal tiling
 
 ©   
Vertex figure [3,4,6,4]
General of army (is itself convex)
Colonel of regiment (is itself locally convex – other uniform tiling member: shothat )
Confer
Grünbaumian relatives:
2rothat  
uniform relative:
trat  
related CRF tilings:
pextrat   pacrothat  
general polytopal classes:
partial Stott expansions  
External
links
wikipedia

This tiling allows for a consistent 3-coloring of the hexagons. When choosing 2 such colors, this would provide way for a partial (tripesic) Stott contraction, resulting in pacrothat.

As abstract polytope rothat is isomorphic to qrothat, therby making both the triangles and the hexagons retrograde.


Incidence matrix according to Dynkin symbol

x3o6x   (N → ∞)

. . . | 6N |  2  2 |  1  2 1
------+----+-------+--------
x . . |  2 | 6N  * |  1  1 0
. . x |  2 |  * 6N |  0  1 1
------+----+-------+--------
x3o . |  3 |  3  0 | 2N  * *
x . x |  4 |  2  2 |  * 3N *
. o6x |  6 |  0  6 |  *  * N

snubbed forms: β3o6x, x3o6s

x3/2o6/5x   (N → ∞)

.   .   . | 6N |  2  2 |  1  2 1
----------+----+-------+--------
x   .   . |  2 | 6N  * |  1  1 0
.   .   x |  2 |  * 6N |  0  1 1
----------+----+-------+--------
x3/2o   . |  3 |  3  0 | 2N  * *
x   .   x |  4 |  2  2 |  * 3N *
.   o6/5x |  6 |  0  6 |  *  * N

s3s6x (N → ∞)

demi( . . . ) | 6N |  1  2  1 |  1 1  2
--------------+----+----------+--------
demi( . . x ) |  2 | 3N  *  * |  0 1  1
sefa( s3s . ) |  2 |  * 6N  * |  1 0  1
sefa( . s6x ) |  2 |  *  * 3N |  0 1  1
--------------+----+----------+--------
      s3s .     3 |  0  3  0 | 2N *  *
      . s6x     6 |  3  0  3 |  * N  *
sefa( s3s6x ) |  4 |  1  2  1 |  * * 3N

starting figure: x3x6x

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