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Tag Archives: icosahedral symmetry
A variant of the Apollonian gasket with icosahedral symmetry
We modify the Apollonian gasket presented in the earlier post Apollonian gasket as a spherical fractal with tetrahedral symmetry. In an icosahedron, five triangles meet at their corners, which gives us a fivefold rotational symmetry. At the centers of the triangles … Continue reading
Posted in Kaleidoscopes, Selfsimilarity, Tilings
Tagged Apollonian gasket, fractal, icosahedral symmetry, spherical geometry, 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