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, 4};
edgeDimTrim=2;
vOverlapColor=True;
pListName="C2=2Cube";
newPTcd={
{1/Sqrt[2], 1/Sqrt[2], 0, 0, 0, 0, 0, 0},
{-(1/Sqrt[2]), 1/Sqrt[2], 0, 0, 0, 0, 0, 0},
{-(1/Sqrt[2]), 1/Sqrt[2], 0, 0, 0, 0, 0, 0};new;

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]];)

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