摘要

描述E8Petrie.svg	English: E8 Petrie projection. This is constructed from VisibLie_E8 found on TheoryOfEverything.org
日期	2010年1月2號
來源	自己作品
作者	Jgmoxness
Other versions	Derivative works of this file:  SimpleTheoryEverything.svg
SVG genesis InfoField	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}

協議

I, the copyright holder of this work, hereby publish it under the following licenses:

呢個檔案用共享創意 姓名標示-非商業性-相同方式分享3.0 未本地化版本條款授權。

你可以：

• 去分享 – 複製、發佈同傳播呢個作品
• 再改 – 創作演繹作品

要遵照下面嘅條件：

• 署名 – 你一定要畀合適嘅表彰、畀返指向呢個授權條款嘅連結，同埋寫明有無改過嚟。你可以用任何合理方式去做，但唔可以用任何方式暗示授權人認可咗你或者你嘅使用方式。
• 相同方式分享 – 如果你用任何方式改過呢個作品，你必須要用返原本或者相似嘅條款發佈。

https://creativecommons.org/licenses/by-sa/3.0CC BY-SA 3.0 Creative Commons Attribution-Share Alike 3.0 truetrue

根據自由軟體基金會發佈嘅無固定段落、封面文字同封底文字GNU自由文件授權條款第1.2或打後嘅版本，你獲授權可以重製、散佈同埋修改爾份文件。授權條款嘅副本喺章節GNU自由文件授權條款。http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue

你可以揀你想用嘅牌照。