E8Petrie.svg
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Summary
Description E8Petrie.svg | |
Date | |
Source | Own work |
Author | Jgmoxness |
Other versions | Derivative works of this file: SimpleTheoryEverything.svg |
SVG development
InfoField
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This diagram was created with
Mathematica
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Detailed description
e8 graph of the Gosset 4 21 polytope as a 2-dimensional skew orthogonal projection inside Petrie polygon. It is an emulation of the hand drawn original by Peter McMullen.
This is the (Petrie) projection in 2-dimensions consisting of the 6720 edges of 8-dimensional length sqrt(2). Edge line colors are varied based on their projected edge lengths.
This is constructed from VisibLie_E8 found on TheoryOfEverything.org archive copy at the Wayback Machine with the following settings:
(* This is an auto generated list from e8Flyer.nb *) new := { scale=0.015; cylR=0.003; range=1.02; showAxes=False; showEdges=True; eGrad=51; edgeVal={Sqrt[2], 6720}; pSize=tiny; ;new;
Also, the 2 projection vectors which produce the diagram from the 240 vertices of this split real even E8 are taken from specific "Richter" rotations of the roots of:
rt[x]:=1+5f[x](1+f[x])
where:
f[x]:=3x^2(x-1)(x+1)
Specifically, these are:
X={0., -0.556793440452, 0.19694925177, -0.19694925177, 0.0805477263944, -0.385290876171, 0., 0.385290876171} Y={0.180913155536, 0., 0.160212955043, 0.160212955043, 0., 0.0990170516545, 0.766360424875, 0.0990170516545}
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