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

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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

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I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

File history

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Date/TimeThumbnailDimensionsUserComment
current15:33, 31 August 2013Thumbnail for version as of 15:33, 31 August 2013807 × 904 (23 KB)Jochen Burghardt (talk | contribs)User created page with UploadWizard

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