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Home > Chaim Goodman-Strauss :: Symmetries
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"Dodecafoam I," by Chaim Goodman-Strauss, University of Arkansas (

Unlike all of the other images in this collection, the symmetry here is not governed by a group action, but rather by a substitution system--a set of replacement rules, based on the stellations of the dodecahedron. Several oddly shaped three-dimensional cells based on the stellations of the dodecahedron are used; a rule then gives a method for dividing each cell into small copies of the others. Such techniques are commonly used to produce highly ordered non-periodic structures; though it may look as if such a structure repeats, in fact it cannot repeat periodically.

cgs-calla.jpg cgs-shells_532.jpg dodecafoam.jpg cgs-morning_glories.jpg cgs-sphere.jpg

American Mathematical Society