Tag Archives: mirror symmetry

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

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Inversion in a single circle

You might think that discussing the inversion in a circle is somewhat underwhelming. But, as I am using multiple inversion in many circles to create fractal images, I found that there are some important ideas you will not find so … Continue reading

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Decorations of semi-regular tessellations

In the last posts I have shown kaleidoscopes that make repeating images in Euclidean, spherical and hyperbolic spaces. They are decorations of regular tilings. But what about semi-regular tilings? Could we decorate them too using mirrors? This would give us … Continue reading

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further wallpapers for hyperbolic space

An equilateral triangle gives us a kaleidoscope of three-fold rotational symmetry. With a square we get two-fold rotational symmetry. Would reflection at the sides of other regular polygons too give periodic images with rotational symmetry ? To get an h-fold … Continue reading

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How to program fast kaleidoscopes

This post repeats parts of earlier posts but I am trying to expand the ideas and explain them better. First, I am showing you how to make rosettes with rotational symmetry and mirror symmetry. This is easier than making kaleidoscopic images, … Continue reading

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The rotational and mirror symmetry at the center

In the last post I used mirror symmetry at two crossing straight lines and the related inversion at a circle. The mirror symmetries generate a k-rotational symmetry for an angle of intersection of π/k. With these symmetries I map any point … Continue reading

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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

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