File:E8Petrie.svg

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Original file(SVG file, nominally 940 × 944 pixels, file size: 1.4 MB)

Summary

Description
English: E8 Petrie projection
Date
Source Own work
Author Jgmoxness
Other versions

Derivative works of this file: SimpleTheoryEverything.svg

Detailed description

e8 graph of the Gosset 421 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 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}

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
w:en:Creative Commons

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GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
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File history

Click on a date/time to view the file as it appeared at that time.

Date/Time Thumbnail Dimensions User Comment
current 16:04, 2 November 2012 Thumbnail for version as of 16:04, 2 November 2012 940 × 944 (1.4 MB) Jgmoxness another try...
15:32, 2 November 2012 Thumbnail for version as of 15:32, 2 November 2012 512 × 512 (980 KB) Jgmoxness Reverted to version as of 15:08, 2 November 2012
15:30, 2 November 2012 Thumbnail for version as of 15:30, 2 November 2012 937 × 941 (1.23 MB) Jgmoxness another try w/white background
15:08, 2 November 2012 Thumbnail for version as of 15:08, 2 November 2012 512 × 512 (980 KB) Jgmoxness Reverted to version as of 14:03, 6 January 2010
15:05, 2 November 2012 Thumbnail for version as of 15:05, 2 November 2012 937 × 941 (1.38 MB) Jgmoxness corrected truncated edges
14:03, 6 January 2010 Thumbnail for version as of 14:03, 6 January 2010 512 × 512 (980 KB) Jgmoxness Made corrections/changes per Talk. Black vertices, full 6720 lines, removed {0,0} centering dot.
23:31, 4 January 2010 Thumbnail for version as of 23:31, 4 January 2010 512 × 512 (588 KB) Tomruen Reverted to version as of 16:34, 3 January 2010
23:29, 4 January 2010 Thumbnail for version as of 23:29, 4 January 2010 512 × 512 (613 KB) Tomruen Reverted to version as of 21:31, 2 January 2010
16:34, 3 January 2010 Thumbnail for version as of 16:34, 3 January 2010 512 × 512 (588 KB) Jgmoxness Slight alteration of edge colors w/correction of edge selection.
21:31, 2 January 2010 Thumbnail for version as of 21:31, 2 January 2010 512 × 512 (613 KB) Jgmoxness {{Information |Description={{en|1=E8 Petrie projection}} |Source={{own}} |Author=Jgmoxness |Date=2010-01-02 |Permission= |other_versions= }}

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