File:Ho-Mg-Zn E8-5Cube.jpg
Summary
This is an image of the electron diffraction pattern of an icosahedral Zn-Mg-Ho QuasiCrystal <a href="//commons.wikimedia.org/wiki/File:Zn-Mg-HoDiffraction.JPG" class="image"><img alt="Zn-Mg-HoDiffraction.JPG" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Zn-Mg-HoDiffraction.JPG/60px-Zn-Mg-HoDiffraction.JPG" width="60" height="61" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Zn-Mg-HoDiffraction.JPG/90px-Zn-Mg-HoDiffraction.JPG 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Zn-Mg-HoDiffraction.JPG/120px-Zn-Mg-HoDiffraction.JPG 2x" data-file-width="364" data-file-height="372"></a> with an overlay of a <a href="https://en.wikipedia.org/wiki/5-cube" class="extiw" title="w:5-cube">5-Cube</a> projection from the 240 vertices of the split real even <a href="https://en.wikipedia.org/wiki/E8_(mathematics)" class="extiw" title="w:E8 (mathematics)">E8</a> Lie Group.
The basis vectors for the E8 projection are shown (1:1 with the ring of gray vertices with the last 3 of 8 dimensions 0). There are 2480 overlapping edge lines from the 240 E8 vertices. They have norm’d unit length calculated from the 5 non-zero projected dimensions of E8. Of these, 32 inner vertices and 80 edges belong to the 5D 5-Cube (Penteract) proper. Edges are shown with colors assigned based on origin vertex distance from the outer perimeter. The vertex colors of the 5-Cube projection represent E8 vertex overlaps. These are:
InView vertices=(color{overlap,count},…)Total
(LightGreen{1,20},Pink{5,20},Gray{10,10},Orange{20,1})51
All vertices=(color{overlap,count},…)Total
(LightGreen{1,20},Pink{5,100},Gray{10,100},Orange{20,20})240
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 10:00, 17 January 2017 | | 1,800 × 1,800 (435 KB) | 127.0.0.1 (talk) | This is an image of the electron diffraction pattern of an icosahedral Zn-Mg-Ho QuasiCrystal <a href="//commons.wikimedia.org/wiki/File:Zn-Mg-HoDiffraction.JPG" class="image"><img alt="Zn-Mg-HoDiffraction.JPG" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Zn-Mg-HoDiffraction.JPG/60px-Zn-Mg-HoDiffraction.JPG" width="60" height="61" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Zn-Mg-HoDiffraction.JPG/90px-Zn-Mg-HoDiffraction.JPG 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Zn-Mg-HoDiffraction.JPG/120px-Zn-Mg-HoDiffraction.JPG 2x" data-file-width="364" data-file-height="372"></a> with an overlay of a <a href="https://en.wikipedia.org/wiki/5-cube" class="extiw" title="w:5-cube">5-Cube</a> projection from the 240 vertices of the split real even <a href="https://en.wikipedia.org/wiki/E8_(mathematics)" class="extiw" title="w:E8 (mathematics)">E<sub>8</sub></a> Lie Group. <br><p>The basis vectors for the E<sub>8</sub> projection are shown (1:1 with the ring of gray vertices with the last 3 of 8 dimensions 0). There are 2480 overlapping edge lines from the 240 E<sub>8</sub> vertices. They have norm’d unit length calculated from the 5 non-zero projected dimensions of E<sub>8</sub>. Of these, 32 inner vertices and 80 edges belong to the 5D 5-Cube (Penteract) proper. Edges are shown with colors assigned based on origin vertex distance from the outer perimeter. The vertex colors of the 5-Cube projection represent E<sub>8</sub> vertex overlaps. These are: <br><br></p> <p>InView vertices=(color{overlap,count},…)Total<br> (LightGreen{1,20},Pink{5,20},Gray{10,10},Orange{20,1})51<br><br> All vertices=(color{overlap,count},…)Total<br></p> (LightGreen{1,20},Pink{5,100},Gray{10,100},Orange{20,20})240 |
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