English: A w:6-cube (w:Hexeract) using 6D w:orthographic_projection to a 3D w:Perspective_(visual) object (the w:Rhombic_triacontahedron) using the w:Golden ratio φ in the w:basis_vectors. This is used to understand the aperiodic w:Icosahedron structure of w:Quasicrystals. This particular projection is used to understand the structure of w:Quasicrystals.

The specific basis vectors are:

x = {1, φ, 0, -1, φ, 0}

y = {φ, 0, 1, φ, 0, -1}

z = {0, 1, φ, 0, -1, φ}

There are 64 vertices and 192 unit length edges forming pentagonal symmetry along specific axis (as well as hexagonal symmetries on other axis). The edge colors are defined by which of the 6 dimensions it aligns with.

This is constructed from VisibLie_E8 found on TheoryOfEverything.org