File:Free modular lattice with 3 generators (x,y,z).gif

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Summary

Description
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
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
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

Licensing

I, the copyright holder of this work, hereby publish it under the following licence:
w:en:Creative Commons
attribution share alike
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Under the following conditions:
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inception

31 August 2013

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Date/TimeThumbnailDimensionsUserComment
current21:03, 31 August 2013Thumbnail for version as of 21:03, 31 August 2013807 × 904 (23 KB)wikimediacommons>Jochen BurghardtUser created page with UploadWizard

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