File:E8Petrie.svg

Original file (SVG file, nominally 512 × 514 pixels, file size: 256 KB)

Summary

Description
English: E8 Petrie projection. This is constructed from VisibLie_E8 found on TheoryOfEverything.org
Date
Source Own work
Author Jgmoxness
Other versions Derivative works of this file:  SimpleTheoryEverything.svg
SVG development
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The SVG code is valid.
 
This diagram was created with Mathematica.

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 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}

Licensing

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Captions

Visual representation of the E8 group

Items portrayed in this file

depicts

2 January 2010

image/svg+xml

File history

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(newest | oldest) View (newer 10 | ) (10 | 20 | 50 | 100 | 250 | 500)
Date/TimeThumbnailDimensionsUserComment
current03:07, 24 March 2022Thumbnail for version as of 03:07, 24 March 2022512 × 514 (256 KB)TSamuelLossless recompression via SVGOMG & vecta.io/nano, & verified via SVGCheck
16:04, 2 November 2012Thumbnail for version as of 16:04, 2 November 2012940 × 944 (1.4 MB)Jgmoxnessanother try...
15:32, 2 November 2012Thumbnail for version as of 15:32, 2 November 2012512 × 512 (980 KB)JgmoxnessReverted to version as of 15:08, 2 November 2012
15:30, 2 November 2012Thumbnail for version as of 15:30, 2 November 2012937 × 941 (1.23 MB)Jgmoxnessanother try w/white background
15:08, 2 November 2012Thumbnail for version as of 15:08, 2 November 2012512 × 512 (980 KB)JgmoxnessReverted to version as of 14:03, 6 January 2010
15:05, 2 November 2012Thumbnail for version as of 15:05, 2 November 2012937 × 941 (1.38 MB)Jgmoxnesscorrected truncated edges
14:03, 6 January 2010Thumbnail for version as of 14:03, 6 January 2010512 × 512 (980 KB)JgmoxnessMade corrections/changes per Talk. Black vertices, full 6720 lines, removed {0,0} centering dot.
23:31, 4 January 2010Thumbnail for version as of 23:31, 4 January 2010512 × 512 (588 KB)TomruenReverted to version as of 16:34, 3 January 2010
23:29, 4 January 2010Thumbnail for version as of 23:29, 4 January 2010512 × 512 (613 KB)TomruenReverted to version as of 21:31, 2 January 2010
16:34, 3 January 2010Thumbnail for version as of 16:34, 3 January 2010512 × 512 (588 KB)JgmoxnessSlight alteration of edge colors w/correction of edge selection.
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