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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.
Source Own work
Author Jgmoxness


I, the copyright holder of this work, hereby publish it under the following license:
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current02:28, 4 October 2017Thumbnail for version as of 02:28, 4 October 20171,383 × 1,360 (484 KB)Tomruen (talk | contribs)crop
16:42, 3 October 2017Thumbnail for version as of 16:42, 3 October 20171,751 × 1,752 (639 KB)Jgmoxness (talk | contribs)Modified edge colors to be defined by which of 6 dimensions the edge aligns with.
17:08, 1 January 2012Thumbnail for version as of 17:08, 1 January 20121,800 × 1,800 (619 KB)Jgmoxness (talk | contribs)lower res
18:30, 29 December 2011Thumbnail for version as of 18:30, 29 December 20112,250 × 2,250 (819 KB)Jgmoxness (talk | contribs)
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