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Tag Archives: tetrahedral symmetry
Apollonian gasket as a spherical fractal with tetrahedral symmetry
Before discussing the relation between the Apollonian gasket and tilings of the sphere, I want to present briefly the spherical kaleidoscope with tetrahedral symmetry. A tetrahedron has three different kinds of points with rotational symmetry. Four equilateral triangles make up … Continue reading
Posted in Anamorphosis, Fractals, Kaleidoscopes, Tilings
Tagged Apollonian gasket, fractal, kaleidoscope, spherical geometry, tetrahedral symmetry, Tiling
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Elliptic kaleidoscopes
In “further hyperbolic kaleidoscopes” I used two straight lines and a circle to make a triangle that defines a kaleidoscope. For k,n and mfold rotational symmetries at its corners, the sum of its three angles is π(1/k+1/n+1/m). If this sum is … Continue reading