File:E8Petrie.svg

[edit] Summary

Detail 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}

[edit] Licensing

I, the copyright holder of this work, hereby publish it under the following licenses: This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. You are free: to share – to copy, distribute and transmit the work to remix – to adapt the work Under the following conditions: attribution – You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work). share alike – If you alter, transform, or build upon this work, you may distribute the resulting work only under the same or similar license to this one. www.creativecommons.org/licenses/by-sa/3.0 CC-BY-SA-3.0 Creative Commons Attribution-Share Alike 3.0 truetrue 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. www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue You may select the license of your choice.

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

	Date/Time	Thumbnail	Dimensions	User	Comment
current	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.
	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= }}

The following file is a duplicate of this file (more details):

• File:E8PetrieFull.svg from Wikimedia Commons

The following page links to this file:

• Paul Erdős

The following other wikis use this file:

• Usage on bg.wikipedia.org
  • Потребител:Stanqo/Математика
• Usage on en.wikipedia.org
  • Coxeter element
  • User:Tomruen/Uniform honeycombs
  • Talk:E8 (mathematics)
  • User:Tomruen/Gosset-Elte figures
  • User talk:Jgmoxness
  • 4 21 polytope
  • User:Jgmoxness
  • User:Tomruen/Kissing number
  • Wikipedia:WikiProject Uniform Polytopes
  • User:Mateuszica/God
• Usage on et.wikipedia.org
  • Kasutaja:Alts
• Usage on sl.wikipedia.org
  • Coxeterjev element