Detail Description:

The specific basis vectors are:

x = {1, φ, 0, -1, φ, 0,0,0}

y = {φ, 0, 1, φ, 0, -1,0,0}

z = {0, 1, φ, 0, -1, φ,0,0}

These are 3 of the 4 basis vectors which fold E8 to H4 and H4 Phi.

This is constructed from VisibLie_E8 found on TheoryOfEverything.org with the following settings:
(* This is an auto generated list from e8Flyer.nb *)
new := {
artPrint=True;
p3D=" 3D";
sliderVal=1.;
cylR=0.005;
scale=0.042;
range=1.7;
shwAxes=False;
limitToRange=False;
showEdges=True;
viewAngle=0.4;
selPrj="E8->H4";
vp=Join[xyVwPnt={1.11, 2.59},{zVwPnt=-1.86}];
};new;

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