Finding the Dual of the Tetrahedral-Octahedral Space Filler
| dc.contributor.author | Knoll, Eva | |
| dc.date.accessioned | 2013-02-08T14:47:52Z | |
| dc.date.available | 2013-02-08T14:47:52Z | |
| dc.date.issued | 2003 | |
| dc.description.abstract | The goal of this paper is to illustrate how octahedra and tetrahedra pack together to fill space, and to identify and visualize the dual to this packing. First, we examine a progression of 2-D and 3-D space-filling packings that relate the tetrahedral-octahedral space-filling packing to the packing of 2-D space by squares. The process will use a combination of stretching, truncation and 2-D to 3-D correspondence. Through slicing, we will also relate certain stages of the process back to simple 2-D packings such as the triangular grid and the 3.6.3.6 Archimedean tiling of the plane. Second, we will illustrate the meaning of duality as it relates to polygons, polyhedra and 2-D and 3-D packings. At a later stage, we will reason out the dual packing of the tetrahedral-octahedral packing. Finally, we will demonstrate that it is indeed a 3-D space filler in its own right by showing different construction methods. | en_US |
| dc.identifier.citation | Knoll, E. (2003). Finding the Dual of the Tetrahedral-Octahedral Space Filler. In Sarhangi, R., (Ed.), Meeting Alhambra, pp. 205-212. | en_US |
| dc.identifier.uri | https://hdl.handle.net/10587/1205 | |
| dc.language.iso | en | en_US |
| dc.publisher | Bridges: Mathematical Connections in Art, Music, and Science | en_US |
| dc.subject | Geometry | en_US |
| dc.subject | Octrahedra | en_US |
| dc.subject | Tetrahedra | en_US |
| dc.title | Finding the Dual of the Tetrahedral-Octahedral Space Filler | en_US |
| dc.type | Conference paper | en_US |