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Volume 35, Number 3, pages 291-294 (2024)
https://doi.org/10.26830/symmetry_2024_3_291
EXHAUSTIVE ENUMERATION OF UNIFORM 3D NETWORKS AND SELF-CLOSE PACKING POLYHEDRA
Michael Burt
Burt Michael, Prof. Emeritus Technion I.I.T, Israel
Email: matburt@netvision.net.il
Abstract: The diversity of space and form which meets the eye is overwhelming. The architecture of the human habitat and the whole domain of physical space structures is mostly concerned with few basic 3D spatial features and their diverse interrelations: Networks-space lattices, Close packing of polyhedral volumetric solids, and Space Dividing Partitions, finite or infinite. These patterns represent the essence of spatial structural morphology. The structure and morphology of any configuration in 3D space might be represented by association of the above-described features. It follows up that: 1) every 3D network is associated with specific polyhedral close packing; 2) every 3D network has a dual construct network, representing interconnection of the centroids of its associated polyhedral, closely packed, solids; 3) every dual network pair is associated with a hyperbolically extending 3D space partition, subdividing the space between the two.
References:
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Wachman, A. Burt, M. Kleinman, M. (1974) Infinite Polyhedra, Technion I.I.T, Israel.
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