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M.C. Escher created a myriad of amazing planar tessellations, yet only a few three-dimensional ones such as his wooden fish ball and dodecahedral flower. We have developed an interactive program to design and manufacture Escher Spheres - sets of tiles that can be assembled into spherical balls. The user chooses from a set of predefined symmetry groups and then deforms the boundaries of the basic domain tile; all corresponding points based on the chosen symmetry class move concurrently, instantly showing the overall result. The interior of the tile can be embellished with a bas-relief. Finally the tile is radially extruded and output as a solid model suitable for free-form fabrication. Categories and Subject Descriptors J.6 Computer Appl.: Computer-Aided Engineering General Terms Computer-aided design (CAD) Keywords M.C. Escher, solid modeling, tessellation, spherical symmetry, spherical tiling, tile editor 1.
Yen et al. (Thu,) studied this question.
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