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Greg Volk
3D Tessellations

Date: 2012-07-26 Time: 19:30 - 22:00 US/Mountain (1 decade 9 months ago)

Where: Albuquerque, NM, United States Venue:


A tessellation is a "space filler", or regular repeated geometric pattern that completely fills a space. In 2D space, the equilateral triangle, square and regular hexagon all qualify as tessellations or space fillers, but the regular pentagon does not. In 3D space, the only Platonic solid (equal edges and faces) that fills space is the cube. However, there are several other 3D shapes that completely fill space, as this demonstration will show. But the really fascinating discovery is that most of the 3D tessellations are related to each other, actually categorized by families of shapes. Moreover each tessellating shape corresponds to a particular packing structure, like body-centered cubic (BCC), face-centered cubic (FCC), or hexoganal close packing (HCP), etc. This demonstration will also explore the duality between the sphere centers of several packing schemes and the vertices of the tessellating shapes that enclose them (aka the Voronoi points). Exhausting the possible packing structures patterns may provide a clue toward determining various characteristics of materials and chemical bonds.