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.

The rotations and reflections which exactly preserve the regular tetrahedron, cube, or icosahedron are applied to the vector perpendicular to one face of the polyhedron to generate the normal vectors to the other faces. As the vector chosen for the first face is altered, 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.