File:Nets for icosahedral aperiodic tile set.svg
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Original file (SVG file, nominally 900 × 523 pixels, file size: 28 KB)
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Summary
| Description |
English: The rhombohedra created when folding these nets form an aperiodic set of tiles under the matching rule that red dots must line up with blue dots. This tile set is due to Alan Mackay and Robert Amman. Different nets of the same tiles are given as Figure 20 in [Lord, Eric A. (1991), “Quasicrystals and Penrose patterns”, in Current Science, volume 61, issue 5, pages 313].
The following asymptote code was used to generate the figure: viewportmargin=(2,2);
size(720);
real t = 2.*cos(pi/5.);
real ph = 31.71747441146101;
real f = 0.4; real r = 0.2;
pair a1 = (1.,0); pair a2 = (0,t);
pair ax1 = rotate(2*ph)*a1; pair ax2 = rotate(2*ph)*a2;
pair ay1 = rotate(180-2*ph)*a1; pair ay2 = rotate(180-2*ph)*a2;
pair b1 = (0,f*t); pair b2 = (0,2*t-f*t);
path rh = (0,0)--(1.,t)--(0,2.*t)--(-1.,t)--cycle;
path d1 = circle(b1,r); path d2 = circle(b2,r);
path p = rh; draw(p,linewidth(1)); fill(p,yellow);
path p = shift(2*a2+2*ay2)*rotate(-4*ph)*rh; draw(p,linewidth(1)); fill(p,yellow);
path p = shift(2*a2)*rotate(180-2*ph)*rh; draw(p,linewidth(1)); fill(p,yellow);
path p = shift(a1+a2)*rh; draw(p,linewidth(1)); fill(p,yellow);
path p = shift(a1+a2)*rotate(-2*ph)*rh; draw(p,linewidth(1)); fill(p,yellow);
path p = shift(a1+a2-2*ay2)*rotate(180-4*ph)*rh; draw(p,linewidth(1)); fill(p,yellow);
path c = d1; draw(c,linewidth(1)); fill(c,brown);
path c = shift(2*a2+2*ay2)*rotate(-4*ph)*d1; draw(c,linewidth(1)); fill(c,brown);
path c = shift(2*a2)*rotate(180-2*ph)*d2; draw(c,linewidth(1)); fill(c,lightblue);
path c = shift(a1+a2)*d2; draw(c,linewidth(1)); fill(c,brown);
path c = shift(a1+a2)*rotate(-2*ph)*d2; draw(c,linewidth(1)); fill(c,lightblue);
path c = shift(a1+a2-2*ay2)*rotate(180-4*ph)*d1; draw(c,linewidth(1)); fill(c,brown);
pair s1 = 2.5*a2;
path p = shift(s1)*rh; draw(p,linewidth(1)); fill(p,yellow);
path p = shift(s1)*shift(2*a2+2*ay2)*rotate(-4*ph)*rh; draw(p,linewidth(1)); fill(p,yellow);
path p = shift(s1)*shift(2*a2)*rotate(180-2*ph)*rh; draw(p,linewidth(1)); fill(p,yellow);
path p = shift(s1)*shift(a1+a2)*rh; draw(p,linewidth(1)); fill(p,yellow);
path p = shift(s1)*shift(a1+a2)*rotate(-2*ph)*rh; draw(p,linewidth(1)); fill(p,yellow);
path p = shift(s1)*shift(a1+a2-2*ay2)*rotate(180-4*ph)*rh; draw(p,linewidth(1)); fill(p,yellow);
path c = shift(s1)*d2; draw(c,linewidth(1)); fill(c,lightblue);
path c = shift(s1)*shift(2*a2+2*ay2)*rotate(-4*ph)*d2; draw(c,linewidth(1)); fill(c,lightblue);
path c = shift(s1)*shift(2*a2)*rotate(180-2*ph)*d1; draw(c,linewidth(1)); fill(c,brown);
path c = shift(s1)*shift(a1+a2)*d1; draw(c,linewidth(1)); fill(c,lightblue);
path c = shift(s1)*shift(a1+a2)*rotate(-2*ph)*d1; draw(c,linewidth(1)); fill(c,brown);
path c = shift(s1)*shift(a2+a1-2*ay2)*rotate(180-4*ph)*d2; draw(c,linewidth(1)); fill(c,lightblue);
pair s2 = 10.1*a1;
path p = shift(s2)*rh; draw(p,linewidth(1)); fill(p,yellow);
path p = shift(s2)*rotate(2*ph)*rh; draw(p,linewidth(1)); fill(p,yellow);
path p = shift(s2)*rotate(-2*ph)*rh; draw(p,linewidth(1)); fill(p,yellow);
path p = shift(s2)*shift(ax1+3*ax2)*rotate(180)*rh; draw(p,linewidth(1)); fill(p,yellow);
path p = shift(s2)*shift(ax1+3*ax2)*rotate(180-2*ph)*rh; draw(p,linewidth(1)); fill(p,yellow);
path p = shift(s2)*shift(ax1+3*ax2)*rotate(180+2*ph)*rh; draw(p,linewidth(1)); fill(p,yellow);
path c = shift(s2)*d1; draw(c,linewidth(1)); fill(c,brown);
path c = shift(s2)*rotate(2*ph)*d1; draw(c,linewidth(1)); fill(c,brown);
path c = shift(s2)*rotate(-2*ph)*d1; draw(c,linewidth(1)); fill(c,lightblue);
path c = shift(s2)*shift(ax1+3*ax2)*rotate(180)*d1; draw(c,linewidth(1)); fill(c,brown);
path c = shift(s2)*shift(ax1+3*ax2)*rotate(180-2*ph)*d1; draw(c,linewidth(1)); fill(c,brown);
path c = shift(s2)*shift(ax1+3*ax2)*rotate(180+2*ph)*d1; draw(c,linewidth(1)); fill(c,lightblue);
pair s3 = 2.5*a2+10.1*a1;
path p = shift(s3)*rh; draw(p,linewidth(1)); fill(p,yellow);
path p = shift(s3)*rotate(2*ph)*rh; draw(p,linewidth(1)); fill(p,yellow);
path p = shift(s3)*rotate(-2*ph)*rh; draw(p,linewidth(1)); fill(p,yellow);
path p = shift(s3)*shift(ax1+3*ax2)*rotate(180)*rh; draw(p,linewidth(1)); fill(p,yellow);
path p = shift(s3)*shift(ax1+3*ax2)*rotate(180-2*ph)*rh; draw(p,linewidth(1)); fill(p,yellow);
path p = shift(s3)*shift(ax1+3*ax2)*rotate(180+2*ph)*rh; draw(p,linewidth(1)); fill(p,yellow);
path c = shift(s3)*d1; draw(c,linewidth(1)); fill(c,lightblue);
path c = shift(s3)*rotate(2*ph)*d1; draw(c,linewidth(1)); fill(c,lightblue);
path c = shift(s3)*rotate(-2*ph)*d1; draw(c,linewidth(1)); fill(c,brown);
path c = shift(s3)*shift(ax1+3*ax2)*rotate(180)*d1; draw(c,linewidth(1)); fill(c,lightblue);
path c = shift(s3)*shift(ax1+3*ax2)*rotate(180-2*ph)*d1; draw(c,linewidth(1)); fill(c,lightblue);
path c = shift(s3)*shift(ax1+3*ax2)*rotate(180+2*ph)*d1; draw(c,linewidth(1)); fill(c,brown);
viewportsize=(720.0pt,0);
|
| Date | |
| Source | Own work |
| Author | Eigenbra |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 03:06, 11 August 2014 | | 900 × 523 (28 KB) | Eigenbra | {{Information |Description ={{en|1=The rhombohedra created when folding these nets form an aperiodic set of tiles under the matching rule that red dots must line up with blue dots. This tile set is due to Alan Mackay and Robert Amman. Different nets... |
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