Acronym
| quishexah |

Name
| hyperbolic quarter order 4 hexagonal-tiling honeycomb |

Circumradius
| sqrt(-2/3) = 0.816497 i |

This non-compact hyperbolic tesselation uses both the euclidean tilings that and trat in the sense of infinite horohedra as some of its cells.

Note, this figure can be considered as being **s4o3o6s'** too. This is quite surprising here, as in general sequential applications of
alternated facetings is *not* commutative! But here we have

- on the one hand: x4o3o6x → s4o3o6x (= x3o3o *b6x) → x3o3o *b6s' (cf. below)
- on the other hand: x4o3o6x → x4o3o6s' (= x4o3x3o3*b) → s4o3x3o3*b (cf. below)

(where both end forms are described below, in turn being equivalent with x3x3o3o3*a3*c). So this provides a rare commutative example, which does not base on an additional symmetry of the starting symbol!

Incidence matrix according to Dynkin symbol

x3x3o3o3*a3*c (N,M,K → ∞) . . . . | 4NMK | 6 3 | 6 3 3 3 | 3 3 1 1 --------------+------+------------+---------------------+---------------- x . . . | 2 | 12NMK * | 1 1 1 0 | 1 1 1 0 . x . . | 2 | * 6NMK | 2 0 0 2 | 2 1 0 1 --------------+------+------------+---------------------+---------------- x3x . . | 6 | 3 3 | 4NMK * * * | 1 1 0 0 x . o . *a3*c | 3 | 3 0 | * 4NMK * * | 1 0 1 0 x . . o3*a | 3 | 3 0 | * * 4NMK * | 0 1 1 0 . x3o . | 3 | 0 3 | * * * 4NMK | 1 0 0 1 --------------+------+------------+---------------------+---------------- x3x3o . *a3*c ♦ 3M | 3M 3M | M M 0 M | 4NK * * * x3x . o3*a ♦ 12 | 12 6 | 4 0 4 0 | * NMK * * x . o3o3*a3*c ♦ K | 3K 0 | 0 K K 0 | * * 4NM * . x3o3o ♦ 4 | 0 6 | 0 0 0 4 | * * * NMK

x3o3o *b6s (N,M,K → ∞) demi( . . . . ) | 4NMK | 3 6 | 3 3 6 3 | 1 3 1 3 -------------------+------+------------+---------------------+---------------- demi( x . . . ) | 2 | 6NMK * | 2 0 2 0 | 1 2 0 1 sefa( . o . *b6s ) | 2 | * 12NMK | 0 1 1 1 | 0 1 1 1 -------------------+------+------------+---------------------+---------------- demi( x3o . . ) | 3 | 3 0 | 4NMK * * * | 1 1 0 0 . o . *b6s | 3 | 0 3 | * 4NMK * * | 0 1 1 0 sefa( x3o . *b6s ) | 6 | 3 3 | * * 4NMK * | 0 1 0 1 sefa( . o3o *b6s ) | 3 | 0 3 | * * * 4NMK | 0 0 1 1 -------------------+------+------------+---------------------+---------------- demi( x3o3o . ) ♦ 4 | 6 0 | 4 0 0 0 |NMK* * * x3o . *b6s ♦ 3M | 3M 3M | M M M 0 | * 4NK * * . o3o *b6s ♦ K | 0 3K | 0 K 0 K | * * 4NM * sefa( x3o3o *b6s ) ♦ 12 | 6 12 | 0 0 4 4 | * * * NMK starting figure: x3o3o *b6x

s4o3x3o3*b (N,M,K → ∞) demi( . . . . ) | 4NMK | 6 3 | 3 3 6 3 | 1 3 1 3 -------------------+------+------------+---------------------+---------------- demi( . . x . ) | 2 | 12NMK * | 1 1 1 0 | 1 1 0 1 s4o . . | 2 | * 6NMK | 0 0 2 2 | 0 1 1 2 -------------------+------+------------+---------------------+---------------- demi( . o3x . ) | 3 | 3 0 | 4NMK * * * | 1 1 0 0 demi( . . x3o ) | 3 | 3 0 | * 4NMK * * | 1 0 0 1 sefa( s4o3x . ) | 6 | 3 3 | * * 4NMK * | 0 1 0 1 sefa( s4o . o3*b ) | 3 | 0 3 | * * * 4NMK | 0 0 1 1 -------------------+------+------------+---------------------+---------------- demi( . o3x3o3*b ) ♦ M | 3M 0 | M M 0 0 |4NK* * * s4o3x . ♦ 12 | 12 6 | 4 0 4 0 | * NMK * * s4o . o3*b ♦ 4 | 0 6 | 0 0 0 4 | * * NMK * sefa( s4o3x3o3*b ) ♦ 3K | 3K 3K | 0 K K K | * * * 4NM starting figure: x4o3x3o3*b

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