Free_modular_lattice_with_3_generators_(x,y,z).gif
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Summary
Description Free modular lattice with 3 generators (x,y,z).gif |
English:
3-dimensional diagram of the free modular lattice generated by {x,y,z}. Constructed in 1900 by R. Dedekind.
O=x∧y∧z, I=x∨y∨z, p=x∧y, p'=x∨y, q=x∧z, q'=x∨z, r=y∧z, r'=y∨z, u=p∨q, u'=p∧q, v=p∨r, v'=p∧r, w=q∨r, w'=q∧r, a=x∧r', a'=x∨r, b=y∧q', b'=y∨q, c=z∧p', c'=z∨p, o=p∨q∨r, i=p'∧q'∧r', e=a∨o=a'∧i, f=b∨o=b'∧i, g=c∨o=c'∧i. |
Date | |
Source | Own work |
Author | Jochen Burghardt |
Gnuplot source code |
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set parametric set hidden3d unset key set xrange [-10:10] set yrange [-10:10] set zrange [-10:10] unset border unset xtics unset ytics unset ztics set style data line set view 30,330,1.0,1.0 set view 55,335,1.0,1.0 set view 25,340,1.0,1.0 set title "Free modular lattice with 3 generators (x,y,z)" font ",16" splot "m28c.gpdat" index 0:08 with lines 1, "m28c.gpdat" index 09:26 with lines 3, "m28c.gpdat" index 27:35 with lines 1, "m28c.gpdat" index 36:38 with lines 1, "m28c.gpdat" index 39:41 with lines 2, "m28c.gpdat" index 42:44 with lines 2, "m28c.gpdat" index 45:47 with lines 1 set label "O" at 0,0,3 front font ",18" tc rgb "#606060" set label "p" at 0,2,3 front font ",18" tc rgb "#606060" set label "q" at 0,0,5 front font ",18" tc rgb "#606060" set label "r" at 2,0,3 front font ",18" tc rgb "#606060" set label "u" at 0,2,5 front font ",18" tc rgb "#606060" set label "v" at 2,2,3 front font ",18" tc rgb "#606060" set label "w" at 2,0,5 front font ",18" tc rgb "#606060" set label "a" at 2,4,5 front font ",18" tc rgb "#606060" set label "b" at 3,3,4 front font ",18" tc rgb "#606060" set label "c" at 4,2,5 front font ",18" tc rgb "#606060" set label "e" at 2,4,7 front font ",18" tc rgb "#606060" set label "f" at 3,3,7 front font ",18" tc rgb "#606060" set label "g" at 4,2,7 front font ",18" tc rgb "#606060" set label "a'" at 4,6,7 front font ",18" tc rgb "#606060" set label "b'" at 4,4,8 front font ",18" tc rgb "#606060" set label "c'" at 6,4,7 front font ",18" tc rgb "#606060" set label "u'" at 5,7,7 front font ",18" tc rgb "#606060" set label "v'" at 5,5,9 front font ",18" tc rgb "#606060" set label "w'" at 7,5,7 front font ",18" tc rgb "#606060" set label "p'" at 5,7,9 front font ",18" tc rgb "#606060" set label "q'" at 7,7,7 front font ",18" tc rgb "#606060" set label "r'" at 7,5,9 front font ",18" tc rgb "#606060" set label "I" at 7,7,9 front font ",18" tc rgb "#606060" set label "o" at 2,2,5 front font ",18" tc rgb "#606060" set label "i" at 5,5,7 front font ",18" tc rgb "#606060" set label "x" at 4,6,5 front font ",18" tc rgb "#000000" set label "y" at 4,4,5 front font ",18" tc rgb "#000000" set label "z" at 6,4,5 front font ",18" tc rgb "#000000" pause -1 "Press Return" |
Data file "m28c.gpdat" used by gnuplot code |
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0 0 3 0 2 3 0 0 3 0 0 5 0 0 3 2 0 3 0 2 3 0 2 5 0 2 3 2 2 3 0 0 5 0 2 5 0 0 5 2 0 5 2 0 3 2 2 3 2 0 3 2 0 5 0 2 5 2 4 5 2 2 3 3 3 4 2 0 5 4 2 5 2 4 5 4 6 5 2 4 5 2 4 7
3 3 4 4 4 5
3 3 4 3 3 7
4 2 5 6 4 5
4 2 5 4 2 7
2 4 7 4 6 7
4 6 5 4 6 7
3 3 7 4 4 8
4 4 5 4 4 8
4 2 7 6 4 7
6 4 5 6 4 7
4 6 7 5 7 7
4 4 8 5 5 9
6 4 7 7 5 7
5 7 7 5 7 9
5 7 7 7 7 7
5 5 9 5 7 9
5 5 9 7 5 9
7 5 7 7 7 7
7 5 7 7 5 9
5 7 9 7 7 9
7 7 7 7 7 9
7 5 9 7 7 9
0 2 5 2 2 5
2 2 3 2 2 5
2 0 5 2 2 5
2 2 5 2 4 7
2 2 5 3 3 7
2 2 5 4 2 7
2 4 7 5 5 7
3 3 7 5 5 7
4 2 7 5 5 7
5 5 7 5 7 7
5 5 7 5 5 9
5 5 7 7 5 7 |
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