Crystalline displays sequences of mutating polyhedra which, although irregular, have an underlying symmetry: the normals to their faces belong to orbits of the tetrahedral, cubic or icosahedral symmetry groups.

To draw these polyhedra, the rotations and reflections which exactly preserve the regular tetrahedron, cube, or icosahedron are applied to some randomly chosen vector to generate the normal vectors to all the faces. As the initial vector is rotated, the shape of the whole polyhedron changes.

The distance of each face from the centre of the polyhedron is also altered, smoothly but arbitrarily, and this means that sometimes faces will be missing, because the chosen distance will put one or more faces outside the convex region defined by the other faces.

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Applets Gallery / Crystalline / created Wednesday, 26 May 2004
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Copyright © Greg Egan, 2004. All rights reserved.