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Truncated order-4 hexagonal tiling with *662 mirror lines. The dual of the tiling represents the fundamental domains of (*662) orbifold symmetry. From [6,6] (*662) symmetry, there are 15 small index subgroup (12 unique) by mirror removal and alternation operators.
The regular map {6,4} 3 or {6,4} (4,0) can be seen as a 4-coloring on the {6,4} tiling. It also has a representation as a petrial octahedron , {3,4} π , an abstract polyhedron with vertices and edges of an octahedron , but instead connected by 4 Petrie polygon faces.
In Coxeter notation can be represented as [1 +,8,8,1 +], (*4444 orbifold) removing two of three mirrors (passing through the square center) in the [8,8] symmetry. The *4444 symmetry can be doubled by bisecting the fundamental domain (square) by a mirror, creating *884 symmetry .
PHOTO: Leah Doherty gifted her father an image composed of the text messages he sent her over several years. (Leah Doherty)
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The regular map {8,3} 2,0 can be seen as a 6-coloring of the {8,3} hyperbolic tiling. Within the regular map, octagons of the same color are considered the same face shown in multiple locations. Within the regular map, octagons of the same color are considered the same face shown in multiple locations.
This symmetry by orbifold notation is called *33333333 with 8 order-3 mirror intersections. In Coxeter notation can be represented as [8*,6], removing two of three mirrors (passing through the octagon center) in the [8,6] symmetry .