Vaguery + symmetry   2

[1007.2460] Polyominoes and Polyiamonds as Fundamental Domains of Isohedral Tilings with Rotational Symmetry
"We describe computer algorithms that produce the complete set of isohedral tilings by n-omino or n-iamond tiles in which the tiles are fundamental domains and the tilings have 3-, 4-, or 6-fold rotational symmetry. The symmetry groups of such tilings are of types p3, p31m, p4, p4g, and p6. There are no isohedral tilings with symmetry groups p3m1, p4m, or p6m that have polyominoes or polyiamonds as fundamental domains. We display the algorithms' output and give enumeration tables for small values of n.…"
computational-geometry  algorithms  mathematical-recreations  group-theory  symmetry  nudge-targets  tiling 
july 2010 by Vaguery
Zwoje (The Scrolls) 44, 2006
"The proposition of the paper is that a direct relation held between the spatial shape of the church, its dedication and the cultural and political situation in the region. These churches inspire further studies of the use of the equilateral triangle plan in architecture, particularly for sacred buildings. In the future such studies should result in a more complete review and perhaps a full catalogue of buildings established on such a plan."
architecture  design  symmetry  churches  nanohistory 
july 2009 by Vaguery

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