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Tag Archives: hyperbolic space
Regular polygons as kaleidoscopes
We are using reflection at the sides of a regular polygon to get a space filling periodic image. Its symmetries depend on the symmetry of the image, which lies inside the polygon. As an example, let us look at the … Continue reading
Posted in Kaleidoscopes, Tilings
Tagged hyperbolic space, mirror symmetry, periodic images, regular polygons, Rotational symmetry
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further wallpapers for hyperbolic space
An equilateral triangle gives us a kaleidoscope of threefold rotational symmetry. With a square we get twofold rotational symmetry. Would reflection at the sides of other regular polygons too give periodic images with rotational symmetry ? To get an hfold … Continue reading
Further hyperbolic kaleidoscopes
In the last post I have used reflections at two parallel lines and a circle to get a Poincaré plane that shows a periodic decoration of hyperbolic space. What happens if the straight lines are not parallel and intersect? Then … Continue reading
Posted in Kaleidoscopes
Tagged hyperbolic space, kaleidoscope, Poincaré disc, rose window, Rotational symmetry
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Variations on the hyperbolic kaleidoscope
In the last post I have presented a hyperbolic kaleidoscope with two and threefold rotational symmetries. Could we have other rotational symmetries? Yes, we simply move the vertical lines! To get an nfold rotational symmetry the circle has to intersect … Continue reading
Posted in Kaleidoscopes
Tagged hyperbolic space, kaleidoscope, Poincaré plane, Rotational symmetry
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A hyperbolic kaleidoscope
In “creating symmetry” Frank Farris shows a wallpaper for hyperbolic space. He uses the Poincaré plane to project the hyperbolic space to our Euclidean drawing surface. The wallpaper then results from mirror symmetries at vertical lines at x=0 and x=0.5 … Continue reading
Posted in Anamorphosis, Kaleidoscopes
Tagged hyperbolic space, inversive geometry, kaleidoscope, mirror symmetry, Poincaré plane
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