A Model of Islamic Rectilinear Interlaced Lattices


LATTICE ORDERS and DISTANCES

Tables

Table 1 - Lattices and their Elementary Figures
N   Theta  a/b    exact        n   Sigmak[i] 
polygons
------------------------------------------------------------------------
6 60 1 1 3 3 1-1-1
4 9 1-22-3
6 12 6*2
------------------------------------------------------------------------
8 45 1.414 Square Root 2 3 4 1-1-2
4 8 4*2, 1-1-1-5, 1-2-2- 3
6 16 11-22-33, 2*(2-3-3), 22- 3333,
11-333-5
8 24 6*3, 4*(1-5)
16 56 8*(1-6), 8*(2-5)
------------------------------------------------------------------------
10 36 1.618 Phi 3 5 1-2-2, 1- 1-3
4 10 22-33, 2-3-2-3, 111- 7,
1-333
6 20 3333-44,
8 30 12222-777, ...
10 40 10*4, ...
20 90 10*(1-8), ...
Table 2 - N-Lattice Ratio
N      a/b     a/b exact
------------------------
6 1 1
8 1.4142 Square Root 2
10 1.6180 (Square Root 5 + 1)/2
12 1.1547
14 1.2470
16 1.1896
18 1.5321


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05-June-95