Finding the Dual of the Tetrahedral-Octahedral Space Filler
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Date
2003
Authors
Knoll, Eva
Journal Title
Journal ISSN
Volume Title
Publisher
Bridges: Mathematical Connections in Art, Music, and Science
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.
Description
Keywords
Geometry , Octrahedra , Tetrahedra
Citation
Knoll, E. (2003). Finding the Dual of the Tetrahedral-Octahedral Space Filler. In Sarhangi, R., (Ed.), Meeting Alhambra, pp. 205-212.