File:7-cubePascal.svg
Original file (SVG file, nominally 681 × 587 pixels, file size: 226 KB)
Captions
Summary[edit]
Description7-cubePascal.svg |
English: 7-Cube in Orthogonal column graph "Pascal Triangle" projection. |
Source | Own work |
Author | Jgmoxness |
Detail Description:
The 8 axes are shown with locators labeled A-H. The 128 vertices are a subset of the E8 group of even (half-integer) permutations. The number of vertices in each column represents rows in Pascal's triangle, being 1:7:21:35:35:21:7:1 in the case of a 7-cube. The 448 edges of unit length have colors that can be varied based on their projected edge positions. The vertex color is varied by overlap counts. Specifically:
vertices={color=overlap,count},...,Total
{{purple=1,32},{black=2,24},{red=3,30},{green=4,32},{blue=5,10}},128
vertices InView={{color=overlap,count},...,Total
{{purple=1,32},{black=2,12},{red=3,10},{green=4,8},{blue=5,2}},64
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=0.06;
cylR=0.021;
range=2.;
limitToRange=False;
favorite=29;
eGrad=0;
showEdges=True;
edgeVal={1, 448};
edgeDimTrim=7;
vOverlapColor=True;
pListName="C7=Even=Int/2";
new;
The 2 projection vectors are:
H={1/Sqrt[7], 1/Sqrt[7], 1/Sqrt[7], 1/Sqrt[7], 1/Sqrt[7], 1/Sqrt[7], 1/Sqrt[7], 0}
V={-(3/(2 Sqrt[7])), -(1/Sqrt[7]), -(1/(2 Sqrt[7])), 0, 1/(2 Sqrt[7]), 1/Sqrt[7], 3/(2 Sqrt[7]), 0}
Credit: User:Tomruen for sharing basis vectors resulting in my code for n-cube Pascal projections:
doCubePascal@n_ := (
H = Normalize@Join[Array[1 &, n],Array[0 &, 8 - n]];
V = Normalize@Join[Table[i, {i, -(n - 1), n - 1, 2}],Array[0 &, 8 - n]];)
Licensing[edit]
- 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 give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
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 |
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 16:43, 5 March 2010 | 681 × 587 (226 KB) | Jgmoxness (talk | contribs) | corrected edges, altered widths/colors | |
04:50, 1 March 2010 | 581 × 499 (770 KB) | Jgmoxness (talk | contribs) | edge overlap used for color (less bold colors as well) | ||
17:22, 28 February 2010 | 581 × 499 (452 KB) | Jgmoxness (talk | contribs) | line thickness | ||
17:12, 28 February 2010 | 581 × 499 (452 KB) | Jgmoxness (talk | contribs) | edge colors | ||
16:49, 28 February 2010 | 581 × 499 (452 KB) | Jgmoxness (talk | contribs) | {{Information |Description={{en|1=7-Cube in Orthogonal "Pascal Triangle" projection.}} |Source={{own}} |Author=Jgmoxness |Date= |Permission= |other_versions= }} |
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