File:E8Petrie.svg
原本檔案 (SVG檔案,表面大細: 512 × 514 像素,檔案大細:256 KB)
Captions
摘要[編輯]
描述E8Petrie.svg | |
日期 | |
來源 | 自己作品 |
作者 | Jgmoxness |
Other versions | Derivative works of this file: SimpleTheoryEverything.svg |
SVG genesis InfoField | This diagram was created with Mathematica. |
Detailed description[編輯]
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}
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檔案歷史
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日期/時間 | 縮圖 | 尺寸 | 用戶 | 註解 | |
---|---|---|---|---|---|
現時 | 2022年3月24號 (四) 03:07 | 512 × 514(256 KB) | TSamuel(傾偈 | 貢獻) | Lossless recompression via SVGOMG & vecta.io/nano, & verified via SVGCheck | |
2012年11月2號 (五) 16:04 | 940 × 944(1.4 MB) | Jgmoxness(傾偈 | 貢獻) | another try... | ||
2012年11月2號 (五) 15:32 | 512 × 512(980 KB) | Jgmoxness(傾偈 | 貢獻) | Reverted to version as of 15:08, 2 November 2012 | ||
2012年11月2號 (五) 15:30 | 937 × 941(1.23 MB) | Jgmoxness(傾偈 | 貢獻) | another try w/white background | ||
2012年11月2號 (五) 15:08 | 512 × 512(980 KB) | Jgmoxness(傾偈 | 貢獻) | Reverted to version as of 14:03, 6 January 2010 | ||
2012年11月2號 (五) 15:05 | 937 × 941(1.38 MB) | Jgmoxness(傾偈 | 貢獻) | corrected truncated edges | ||
2010年1月6號 (三) 14:03 | 512 × 512(980 KB) | Jgmoxness(傾偈 | 貢獻) | Made corrections/changes per Talk. Black vertices, full 6720 lines, removed {0,0} centering dot. | ||
2010年1月4號 (一) 23:31 | 512 × 512(588 KB) | Tomruen(傾偈 | 貢獻) | Reverted to version as of 16:34, 3 January 2010 | ||
2010年1月4號 (一) 23:29 | 512 × 512(613 KB) | Tomruen(傾偈 | 貢獻) | Reverted to version as of 21:31, 2 January 2010 | ||
2010年1月3號 (日) 16:34 | 512 × 512(588 KB) | Jgmoxness(傾偈 | 貢獻) | Slight alteration of edge colors w/correction of edge selection. |
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