#Desargues' two triangle theorem represented as a graph
#The red and blue nodes represent points and lines.
#See file for more info.
#by
# Desargues graph laid on 4-dim regular 5-tope (not shown here, see desarg5.rot).
# Cyan nodes are on mid-edges, and yellow nodes on mid-faces of the 5-tope.
#
# The graph shows the points and lines (the two color nodes) in
# the 5th Axiom of Incidence (Proj. Geometry).
#
# Graph by Xah Lee, 4dim. model by
#
# Not all the symmetry is visible in 3-d, for instance the links that
# persist in being shorter than the rest are simply mainly in the
# w-direction and have only a short projection in x,y,z.
# edges of 5-tope points
#
# 0 0 0 0 0
#
#+6 +6 -6 3 to 1
#+6 -6 +6 3 to 2
#-6 +6 +6 3 to 3
#-6 -6 -6 3 to 4
# 0 0 0 3 to 0
#
#+6 -6 +6 3 to 2
#-6 -6 -6 3 to 4
#+6 +6 -6 3 to 1
#-6 +6 +6 3 to 3
# 0 0 0 3 to 0
# midedges nodes
-6 0 0 -1 43 R'
-6 0 0 0
-4 +1 -1 2 to q
-6 0 0 0
-4 -1 +1 2 to p
-6 0 0 0
-5 0 0 2 to a3
0 -6 0 -1 42 Q'
0 -6 0 0
-1 -4 +1 2 to p
0 -6 0 0
+1 -4 -1 2 to r
0 -6 0 0
0 -5 0 2 to a2
0 0 -6 -1 41 P'
0 0 -6 0
+1 -1 -4 2 to r
0 0 -6 0
-1 +1 -4 2 to q
0 0 -6 0
0 0 -5 2 to a1
+6 0 0 -1 21 A3
+6 0 0 0
+5 0 0 2 to r'
+6 0 0 0
+4 -1 -1 2 to r
+6 0 0 0
+4 +1 +1 2 to s
0 +6 0 -1 32 A2
0 +6 0 0
0 +5 0 2 to q'
0 +6 0 0
-1 +4 -1 2 to q
0 +6 0 0
+1 +4 +1 2 to s
0 0 +6 -1 13 A1
0 0 +6 0
0 0 +5 2 to p'
0 0 +6 0
-1 -1 +4 2 to p
0 0 +6 0
+1 +1 +4 2 to s
-3 -3 -3 -1 04 S
-3 -3 -3 0
-3.5 -1.5 -1.5 2 to a3
-3 -3 -3 0
-1.5 -3.5 -1.5 2 to a2
-3 -3 -3 0
-1.5 -1.5 -3.5 2 to a1
-3 +3 +3 -1 03 R
-3 +3 +3 0
-1.5 +3.5 +1.5 2 to q'
-3 +3 +3 0
-1.5 +1.5 +3.5 2 to p'
-3 +3 +3 0
-3.5 +1.5 +1.5 2 to a3
+3 -3 +3 -1 02 Q
+3 -3 +3 0
+1.5 -1.5 +3.5 2 to p'
+3 -3 +3 0
+3.5 -1.5 +1.5 2 to r'
+3 -3 +3 0
+1.5 -3.5 +1.5 2 to a2
+3 +3 -3 -1 01 P
+3 +3 -3 0
+1.5 +3.5 -1.5 2 to q'
+3 +3 -3 0
+3.5 +1.5 -1.5 2 to r'
+3 +3 -3 0
+1.5 +1.5 -3.5 2 to a3
# midfaces nodes
+2 -2 -2 -3 421 r
+2 -2 -2 0
+1 -1 -4 2 to P'
+2 -2 -2 0
+1 -4 -1 2 to Q'
+2 -2 -2 0
+4 -1 -1 2 to A3
-2 +2 -2 -3 413 q
-2 +2 -2 0
-4 +1 -1 2 to R'
-2 +2 -2 0
-1 +1 -4 2 to P'
-2 +2 -2 0
-1 +4 -1 2 to a2
-2 -2 +2 -3 432 p
-2 -2 +2 0
-1 -4 +1 2 to Q'
-2 -2 +2 0
-4 -1 +1 2 to R'
-2 -2 +2 0
-1 -1 +4 2 to a1
+2 +2 +2 -3 321 s
+2 +2 +2 0
+4 +1 +1 2 to A3
+2 +2 +2 0
+1 +4 +1 2 to A2
+2 +2 +2 0
+1 +1 +4 2 to A1
+4 0 0 -3 021 r'
+4 0 0 0
+3.5 -1.5 +1.5 2 to Q
+4 0 0 0
+3.5 +1.5 -1.5 2 to P
+4 0 0 0
+5 0 0 2 to A3
0 +4 0 -3 013 q'
0 +4 0 0
-1.5 +3.5 +1.5 2 to R
0 +4 0 0
+1.5 +3.5 -1.5 2 to P
0 +4 0 0
0 +5 0 2 to A2
0 0 +4 -3 032 p'
0 0 +4 0
+1.5 -1.5 +3.5 2 to Q
0 0 +4 0
-1.5 +1.5 +3.5 2 to R
0 0 +4 0
0 0 +5 2 to A1
-4 0 0 -3 430 a3
-4 0 0 0
-5 0 0 2 to R'
-4 0 0 0
-3.5 +1.5 +1.5 2 to R
-4 0 0 0
-3.5 -1.5 -1.5 2 to S
0 -4 0 -3 420 a2
0 -4 0 0
0 -5 0 2 to Q'
0 -4 0 0
+1.5 -3.5 +1.5 2 to Q
0 -4 0 0
-1.5 -3.5 -1.5 2 to S
0 0 -4 -3 410 a1
0 0 -4 0
0 0 -5 2 to P'
0 0 -4 0
+1.5 +1.5 -3.5 2 to P
0 0 -4 0
-1.5 -1.5 -3.5 2 to S