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Its checkerboard coloring can be called a octaoctagonal tiling, and Schläfli ... [8,8] kaleidoscope. Removing the mirror between the order 2 and 4 points, [8,8,1 ...
A toy kaleidoscope. A kaleidoscope (/ k ə ˈ l aɪ d ə s k oʊ p /) is an optical instrument with two or more reflecting surfaces (or mirrors) tilted to each other at an angle, so that one or more (parts of) objects on one end of these mirrors are shown as a symmetrical pattern when viewed from the other end, due to repeated reflection.
The dual tiling has face configuration V6.8.6.8, and represents the fundamental domains of a quadrilateral kaleidoscope, orbifold (*4343), shown here. Adding a 2-fold gyration point at the center of each rhombi defines a (2*43) orbifold.
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This tiling represents a hyperbolic kaleidoscope of 6 mirrors defining a regular hexagon fundamental domain, and 5 mirrors meeting at a point. This symmetry by orbifold notation is called *33333 with 5 order-3 mirror intersections.
This tiling represents a hyperbolic kaleidoscope of 8 mirrors meeting at a point and bounding regular octagon fundamental domains. This symmetry by orbifold notation is called *33333333 with 8 order-3 mirror intersections.
This tiling represents a hyperbolic kaleidoscope of 6 mirrors defining a regular hexagon fundamental domain. This symmetry by orbifold notation is called *333333 with 6 order-3 mirror intersections. In Coxeter notation can be represented as [6 * ,6], removing two of three mirrors (passing through the hexagon center) in the [6,6] symmetry.
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