In the tiling above, \(p\) is the number of vertices of each polygon, and \(q\) is the number of polygons adjacent to each vertex. Reflecting any of its neighbours can create every polygon. The first reflections are shown as arrows in the figure below. Reflecting a polygon in all its edges and then repeatedly reflecting each newly created polygon in its The circle itself is not included in the universe but can be seen as the circle at infinity.įor a regular hyperbolic polygon, all angles are equal, and all sides have the Which is commonly called the Poincaré disc. The inside of \(C_\infty\) is the hyperbolic universe, The tiling is made of regular hyperbolic polygons inside a circle \(C_\infty\). Drag the white dots! Choose rendering style! Hide/show dots! Pick p and q!
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