File:E8Petrie.svg
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Summary
DescriptionE8Petrie.svg | |
Date | |
Source | Own work |
Author | Jgmoxness |
Other versions | Derivative works of this file: SimpleTheoryEverything.svg |
SVG development InfoField | 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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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.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
Items portrayed in this file
depicts
2 January 2010
image/svg+xml
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 03:07, 24 March 2022 | 512 × 514 (256 KB) | TSamuel | Lossless recompression via SVGOMG & vecta.io/nano, & verified via SVGCheck | |
16:04, 2 November 2012 | 940 × 944 (1.4 MB) | Jgmoxness | another try... | ||
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 | 937 × 941 (1.23 MB) | Jgmoxness | another try w/white background | ||
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 | 937 × 941 (1.38 MB) | Jgmoxness | corrected truncated edges | ||
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 | 512 × 512 (588 KB) | Tomruen | Reverted to version as of 16:34, 3 January 2010 | ||
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 | 512 × 512 (588 KB) | Jgmoxness | Slight alteration of edge colors w/correction of edge selection. |
File usage
- 4 21 polytope
- Adjoint representation
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- Borel–de Siebenthal theory
- Cartan matrix
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- Circle group
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- Talk:E8 (mathematics)/Archive 1
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- Talk:Representation theory of the Lorentz group
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