File:PG3-2-configuration.gif
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Summary
| Description |
English: PG(3,2) configuration in a tetrahedron, 15 points, 35 "lines".
There are 15 red vertices: 4 corners (v), 6 mid-edge (e), 4 mid-face (f), and 1 central (c). It has 35 "lines" colored by positions: 6 vev (green), 12 vfe (blue), 4 eee (red circles), 4 vcf (magenta), 3 ece (yellow), 6 eff (cyan circles). |
| Date | |
| Source | Own work |
| Author | Tomruen |
Data
Numbering the points 0...14 (4 corners (v), 6 mid-edges (e), 4 mid-faces (f), and 1 central (c)), the 35 lines of the configuration can be grouped by symmetry positions in the tetrahedron:
| 6 v2e | 12 vef | 4 e3 | 4 vfc | 3 e2c | 6 ef2 | |||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 1 | 2 | 0 | 0 | 0 | 1 | 1 | 1 | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 5 | 7 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 4 | 5 | 6 | 7 | 8 | 9 |
| 1 | 2 | 3 | 2 | 3 | 3 | 7 | 8 | 9 | 5 | 6 | 9 | 4 | 6 | 8 | 4 | 5 | 7 | 5 | 6 | 6 | 8 | 13 | 12 | 11 | 10 | 9 | 8 | 7 | 12 | 11 | 10 | 11 | 10 | 10 |
| 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 10 | 11 | 13 | 10 | 12 | 13 | 11 | 12 | 13 | 7 | 8 | 9 | 9 | 14 | 14 | 14 | 14 | 14 | 14 | 14 | 13 | 13 | 13 | 12 | 12 | 11 |
Plane elements not shown. Each set of vertices contain a Fano plane with incident lines above.
| 4 v3e3f | 6 v2e2f2c | 4 ve3f3 | 1 e6c | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 2 | 0 | 1 | 2 | 3 | 4 |
| 1 | 1 | 2 | 2 | 1 | 2 | 3 | 2 | 3 | 3 | 7 | 5 | 4 | 4 | 5 |
| 2 | 3 | 3 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 8 | 6 | 6 | 5 | 6 |
| 4 | 4 | 5 | 7 | 9 | 8 | 7 | 6 | 8 | 4 | 9 | 9 | 8 | 7 | 7 |
| 5 | 6 | 6 | 8 | 12 | 11 | 10 | 11 | 10 | 10 | 10 | 10 | 10 | 11 | 8 |
| 7 | 8 | 9 | 9 | 13 | 13 | 13 | 12 | 12 | 11 | 11 | 13 | 12 | 12 | 9 |
| 10 | 11 | 12 | 13 | 14 | 14 | 14 | 14 | 14 | 14 | 12 | 13 | 13 | 13 | 14 |
Stored as an en:OFF (file format):
OFF # PG(3,2), higher Fano plane 15 15 35 # points, planes, lines 0 0 0 255 0 0 # name=v0 6 6 0 255 0 0 # name=v1 6 0 6 255 0 0 # name=v2 0 6 6 255 0 0 # name=v3 3 3 0 255 0 0 # name=v01 3 0 3 255 0 0 # name=v02 0 3 3 255 0 0 # name=v03 6 3 3 255 0 0 # name=v12 3 6 3 255 0 0 # name=v13 3 3 6 255 0 0 # name=v23 4 2 2 255 0 0 # name=v012 2 4 2 255 0 0 # name=v013 2 2 4 255 0 0 # name=v023 4 4 4 255 0 0 # name=v123 3 3 3 255 0 0 # name=v0123 7 0 1 2 4 5 7 10 187 0 0 # name=vvveeef1 #hide 7 0 1 3 4 6 8 11 187 0 0 # name=vvveeef2 #hide 7 0 2 3 5 6 9 12 187 0 0 # name=vvveeef3 #hide 7 1 2 3 7 8 9 13 187 0 0 # name=vvveeef4 #hide 7 0 1 4 9 12 13 14 255 255 0 # name=vveeffc1 #hide 7 0 2 5 8 11 13 14 255 255 0 # name=vveeffc2 #hide 7 0 3 6 7 10 13 14 255 255 0 # name=vveeffc3 #hide 7 1 2 7 6 11 12 14 255 255 0 # name=vveeffc4 #hide 7 1 3 8 5 10 12 14 255 255 0 # name=vveeffc5 #hide 7 2 3 9 4 10 11 14 255 255 0 # name=vveeffc6 #hide 7 0 7 8 9 10 11 12 0 255 0 # name=veeeffc1 #hide 7 1 5 6 9 10 11 13 0 255 0 # name=vveeffc2 #hide 7 2 4 6 8 10 12 13 0 255 0 # name=vveeffc3 #hide 7 3 4 5 7 11 12 13 0 255 0 # name=vveeffc4 #hide 7 4 5 6 7 8 9 14 255 0 255 # name=eeeeeec1 #hide 3 0 1 4 0 255 0 # name=vev1 3 0 2 5 0 255 0 # name=vev2 3 0 3 6 0 255 0 # name=vev3 3 1 2 7 0 255 0 # name=vev4 3 1 3 8 0 255 0 # name=vev5 3 2 3 9 0 255 0 # name=vev6 3 0 7 10 0 0 255 # name=vfe1 3 0 8 11 0 0 255 # name=vfe2 3 0 9 12 0 0 255 # name=vfe3 3 1 5 10 0 0 255 # name=vfe4 3 1 6 11 0 0 255 # name=vfe5 3 1 9 13 0 0 255 # name=vfe6 3 2 4 10 0 0 255 # name=vfe7 3 2 6 12 0 0 255 # name=vfe8 3 2 8 13 0 0 255 # name=vfe9 3 3 4 11 0 0 255 # name=vfe10 3 3 5 12 0 0 255 # name=vfe11 3 3 7 13 0 0 255 # name=vfe12 3 4 5 7 187 0 0 # name=eee1 3 4 6 8 187 0 0 # name=eee2 3 5 6 9 187 0 0 # name=eee3 3 7 8 9 187 0 0 # name=eee4 3 0 13 14 255 0 255 # name=vcf1 3 1 12 14 255 0 255 # name=vcf2 3 2 11 14 255 0 255 # name=vcf3 3 3 10 14 255 0 255 # name=vcf4 3 4 9 14 255 255 0 # name=ece1 3 5 8 14 255 255 0 # name=ece2 3 6 7 14 255 255 0 # name=ece3 3 4 12 13 0 255 255 # name=eff1 3 5 11 13 0 255 255 # name=eff2 3 6 10 13 0 255 255 # name=eff3 3 7 11 12 0 255 255 # name=eff4 3 8 10 12 0 255 255 # name=eff5 3 9 10 11 0 255 255 # name=eff6
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
 
|
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 08:59, 12 April 2025 | | 640 × 640 (16.99 MB) | wikimediacommons>Tomruen | Fix blue to magenta |
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