File:3-cubePascal.svg

Summary

Description
English: 3-Cube in column projection showing Pascal Triangle vertex counts in each column. Vertex colors are colored based on overlaps (if any). Edges are colored based on vertex positions. Axes dimensions are shown.
Source Own work
Author Jgmoxness

Source code

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;
showEdges=True;
eGrad=0;
edgeVal={1, 12};
edgeDimTrim=3;
vOverlapColor=True;
pListName="C3=3Cube";
newPTcd={
{1/Sqrt[3], 1/Sqrt[3], 1/Sqrt[3], 0, 0, 0, 0, 0},
{-(1/Sqrt[2]), 0, 1/Sqrt[2], 0, 0, 0, 0, 0},
{-(1/Sqrt[2]), 0, 1/Sqrt[2], 0, 0, 0, 0, 0}};
};new;

Credit: User_talk: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

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Category:Self-published work Category:Algebraic topology Category:Hypercube graphs#3 Category:Cube projections Category:2-fold rotational symmetry Category:Geometry images with dihedral symmetry#02 Category:Images with Mathematica source code
Category:2-fold rotational symmetry Category:Algebraic topology Category:CC-BY-SA-3.0 Category:Cube projections Category:GFDL Category:Geometry images with dihedral symmetry Category:Hypercube graphs Category:Images with Mathematica source code Category:License migration redundant Category:Self-published work