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©
- general polytopal classes:
- Wythoffian polytera
| Acronym | garcornit |
| Name | great retrocellirhombated penteractitriacontaditeron |
| Field of sections |
|
| Circumradius | sqrt[17-8 sqrt(2)]/2 = 1.192297 |
| Vertex figure |
|
| Coordinates | (2 sqrt(2)-1, sqrt(2)-1, sqrt(2)-1, 1, 1)/2 & all permutations, all changes of sign |
| Colonel of regiment | wacbinant |
| Face vector | 960, 3840, 3920, 1280, 142 |
| Confer |
|
As abstract polytope garcornit is isomorphic to recarnit, thereby replacing octagrams by octagons, resp. gocco by socco, quith by tic, and quitco by girco, resp. wavitoth by rawvatoth, gichado by sichado, and giphado by siphado.
Incidence matrix according to Dynkin symbol
4
x---o
4/3 \ / 3
x
3 / \ 3
x---o
3/2
x4/3x4o3*a3o3/2x3*a . . . . . | 960 | 4 2 2 | 4 2 2 4 1 4 1 | 2 2 4 1 2 2 2 2 | 1 2 2 1 1 --------------------+-----+--------------+-----------------------------+------------------------------+--------------- x . . . . | 2 | 1920 * * | 1 1 1 1 0 0 0 | 1 1 1 1 1 1 0 0 | 1 1 1 1 0 . x . . . | 2 | * 960 * | 2 0 0 0 1 2 0 | 2 1 2 0 0 0 2 1 | 1 2 1 0 1 . . . . x | 2 | * * 960 | 0 0 0 2 0 2 1 | 0 0 2 0 1 2 1 2 | 0 1 2 1 1 --------------------+-----+--------------+-----------------------------+------------------------------+--------------- x4/3x . . . | 8 | 4 4 0 | 480 * * * * * * | 1 1 1 0 0 0 0 0 | 1 1 1 0 0 x . o3*a . . | 3 | 3 0 0 | * 640 * * * * * | 1 0 0 1 1 0 0 0 | 1 1 0 1 0 x . . *a3o . | 3 | 3 0 0 | * * 640 * * * * | 0 1 0 1 0 1 0 0 | 1 0 1 1 0 x . . . x3*a | 6 | 3 0 3 | * * * 640 * * * | 0 0 1 0 1 1 0 0 | 0 1 1 1 0 . x4o . . | 4 | 0 4 0 | * * * * 240 * * | 2 0 0 0 0 0 2 0 | 1 2 0 0 1 . x . . x | 4 | 0 2 2 | * * * * * 960 * | 0 0 1 0 0 0 1 1 | 0 1 1 0 1 . . . o3/2x | 3 | 0 0 3 | * * * * * * 320 | 0 0 0 0 0 2 0 2 | 0 0 2 1 1 --------------------+-----+--------------+-----------------------------+------------------------------+--------------- x4/3x4o3*a . . ♦ 24 | 24 24 0 | 6 8 0 0 6 0 0 | 80 * * * * * * * | 1 1 0 0 0 x4/3x . *a3o . ♦ 24 | 24 12 0 | 6 0 8 0 0 0 0 | * 80 * * * * * * | 1 0 1 0 0 x4/3x . . x3*a ♦ 48 | 24 24 24 | 6 0 0 8 0 12 0 | * * 80 * * * * * | 0 1 1 0 0 x . o3*a3o . ♦ 6 | 12 0 0 | 0 4 4 0 0 0 0 | * * * 160 * * * * | 1 0 0 1 0 x . o3*a . x3*a ♦ 12 | 12 0 6 | 0 4 0 4 0 0 0 | * * * * 160 * * * | 0 1 0 1 0 x . . *a3o3/2x3*a ♦ 12 | 12 0 12 | 0 0 4 4 0 0 4 | * * * * * 160 * * | 0 0 1 1 0 . x4o . x ♦ 8 | 0 8 4 | 0 0 0 0 2 4 0 | * * * * * * 240 * | 0 1 0 0 1 . x . o3/2x ♦ 6 | 0 3 6 | 0 0 0 0 0 3 2 | * * * * * * * 320 | 0 0 1 0 1 --------------------+-----+--------------+-----------------------------+------------------------------+--------------- x4/3x4o3*a3o . ♦ 96 | 192 96 0 | 48 64 64 0 24 0 0 | 8 8 0 16 0 0 0 0 | 10 * * * * x4/3x4o3*a . x3*a ♦ 192 | 192 192 96 | 48 64 0 64 48 96 0 | 8 0 8 0 16 0 24 0 | * 10 * * * x4/3x . *a3o3/2x3*a ♦ 192 | 192 96 192 | 48 0 64 64 0 96 64 | 0 8 8 0 0 16 0 32 | * * 10 * * x . o3*a3o3/2x3*a ♦ 30 | 60 0 30 | 0 20 20 20 0 0 10 | 0 0 0 5 5 5 0 0 | * * * 32 * . x4o o3/2x ♦ 12 | 0 12 12 | 0 0 0 0 3 12 4 | 0 0 0 0 0 0 3 4 | * * * * 80
4/3
x---o
4/3 \ / 3/2
x
3 / \ 3
x---o
3/2
x4/3x4/3o3/2*a3o3/2x3*a . . . . . | 960 | 4 2 2 | 4 2 2 4 1 4 1 | 2 2 4 1 2 2 2 2 | 1 2 2 1 1 ------------------------+-----+--------------+-----------------------------+------------------------------+--------------- x . . . . | 2 | 1920 * * | 1 1 1 1 0 0 0 | 1 1 1 1 1 1 0 0 | 1 1 1 1 0 . x . . . | 2 | * 960 * | 2 0 0 0 1 2 0 | 2 1 2 0 0 0 2 1 | 1 2 1 0 1 . . . . x | 2 | * * 960 | 0 0 0 2 0 2 1 | 0 0 2 0 1 2 1 2 | 0 1 2 1 1 ------------------------+-----+--------------+-----------------------------+------------------------------+--------------- x4/3x . . . | 8 | 4 4 0 | 480 * * * * * * | 1 1 1 0 0 0 0 0 | 1 1 1 0 0 x . o3/2*a . . | 3 | 3 0 0 | * 640 * * * * * | 1 0 0 1 1 0 0 0 | 1 1 0 1 0 x . . *a3o . | 3 | 3 0 0 | * * 640 * * * * | 0 1 0 1 0 1 0 0 | 1 0 1 1 0 x . . . x3*a | 6 | 3 0 3 | * * * 640 * * * | 0 0 1 0 1 1 0 0 | 0 1 1 1 0 . x4/3o . . | 4 | 0 4 0 | * * * * 240 * * | 2 0 0 0 0 0 2 0 | 1 2 0 0 1 . x . . x | 4 | 0 2 2 | * * * * * 960 * | 0 0 1 0 0 0 1 1 | 0 1 1 0 1 . . . o3/2x | 3 | 0 0 3 | * * * * * * 320 | 0 0 0 0 0 2 0 2 | 0 0 2 1 1 ------------------------+-----+--------------+-----------------------------+------------------------------+--------------- x4/3x4/3o3/2*a . . ♦ 24 | 24 24 0 | 6 8 0 0 6 0 0 | 80 * * * * * * * | 1 1 0 0 0 x4/3x . *a3o . ♦ 24 | 24 12 0 | 6 0 8 0 0 0 0 | * 80 * * * * * * | 1 0 1 0 0 x4/3x . . x3*a ♦ 48 | 24 24 24 | 6 0 0 8 0 12 0 | * * 80 * * * * * | 0 1 1 0 0 x . o3/2*a3o . ♦ 6 | 12 0 0 | 0 4 4 0 0 0 0 | * * * 160 * * * * | 1 0 0 1 0 x . o3/2*a . x3*a ♦ 12 | 12 0 6 | 0 4 0 4 0 0 0 | * * * * 160 * * * | 0 1 0 1 0 x . . *a3o3/2x3*a ♦ 12 | 12 0 12 | 0 0 4 4 0 0 4 | * * * * * 160 * * | 0 0 1 1 0 . x4/3o . x ♦ 8 | 0 8 4 | 0 0 0 0 2 4 0 | * * * * * * 240 * | 0 1 0 0 1 . x . o3/2x ♦ 6 | 0 3 6 | 0 0 0 0 0 3 2 | * * * * * * * 320 | 0 0 1 0 1 ------------------------+-----+--------------+-----------------------------+------------------------------+--------------- x4/3x4/3o3/2*a3o . ♦ 96 | 192 96 0 | 48 64 64 0 24 0 0 | 8 8 0 16 0 0 0 0 | 10 * * * * x4/3x4/3o3/2*a . x3*a ♦ 192 | 192 192 96 | 48 64 0 64 48 96 0 | 8 0 8 0 16 0 24 0 | * 10 * * * x4/3x . *a3o3/2x3*a ♦ 192 | 192 96 192 | 48 0 64 64 0 96 64 | 0 8 8 0 0 16 0 32 | * * 10 * * x . o3/2*a3o3/2x3*a ♦ 30 | 60 0 30 | 0 20 20 20 0 0 10 | 0 0 0 5 5 5 0 0 | * * * 32 * . x4/3o o3/2x ♦ 12 | 0 12 12 | 0 0 0 0 3 12 4 | 0 0 0 0 0 0 3 4 | * * * * 80
4
x---o
4/3 \ / 3
x
3 / \ 3/2
x---o
3
x4/3x4o3*a3/2o3x3*a . . . . . | 960 | 4 2 2 | 4 2 2 4 1 4 1 | 2 2 4 1 2 2 2 2 | 1 2 2 1 1 --------------------+-----+--------------+-----------------------------+------------------------------+--------------- x . . . . | 2 | 1920 * * | 1 1 1 1 0 0 0 | 1 1 1 1 1 1 0 0 | 1 1 1 1 0 . x . . . | 2 | * 960 * | 2 0 0 0 1 2 0 | 2 1 2 0 0 0 2 1 | 1 2 1 0 1 . . . . x | 2 | * * 960 | 0 0 0 2 0 2 1 | 0 0 2 0 1 2 1 2 | 0 1 2 1 1 --------------------+-----+--------------+-----------------------------+------------------------------+--------------- x4/3x . . . | 8 | 4 4 0 | 480 * * * * * * | 1 1 1 0 0 0 0 0 | 1 1 1 0 0 x . o3*a . . | 3 | 3 0 0 | * 640 * * * * * | 1 0 0 1 1 0 0 0 | 1 1 0 1 0 x . . *a3/2o . | 3 | 3 0 0 | * * 640 * * * * | 0 1 0 1 0 1 0 0 | 1 0 1 1 0 x . . . x3*a | 6 | 3 0 3 | * * * 640 * * * | 0 0 1 0 1 1 0 0 | 0 1 1 1 0 . x4o . . | 4 | 0 4 0 | * * * * 240 * * | 2 0 0 0 0 0 2 0 | 1 2 0 0 1 . x . . x | 4 | 0 2 2 | * * * * * 960 * | 0 0 1 0 0 0 1 1 | 0 1 1 0 1 . . . o3x | 3 | 0 0 3 | * * * * * * 320 | 0 0 0 0 0 2 0 2 | 0 0 2 1 1 --------------------+-----+--------------+-----------------------------+------------------------------+--------------- x4/3x4o3*a . . ♦ 24 | 24 24 0 | 6 8 0 0 6 0 0 | 80 * * * * * * * | 1 1 0 0 0 x4/3x . *a3/2o . ♦ 24 | 24 12 0 | 6 0 8 0 0 0 0 | * 80 * * * * * * | 1 0 1 0 0 x4/3x . . x3*a ♦ 48 | 24 24 24 | 6 0 0 8 0 12 0 | * * 80 * * * * * | 0 1 1 0 0 x . o3*a3/2o . ♦ 6 | 12 0 0 | 0 4 4 0 0 0 0 | * * * 160 * * * * | 1 0 0 1 0 x . o3*a . x3*a ♦ 12 | 12 0 6 | 0 4 0 4 0 0 0 | * * * * 160 * * * | 0 1 0 1 0 x . . *a3/2o3x3*a ♦ 12 | 12 0 12 | 0 0 4 4 0 0 4 | * * * * * 160 * * | 0 0 1 1 0 . x4o . x ♦ 8 | 0 8 4 | 0 0 0 0 2 4 0 | * * * * * * 240 * | 0 1 0 0 1 . x . o3x ♦ 6 | 0 3 6 | 0 0 0 0 0 3 2 | * * * * * * * 320 | 0 0 1 0 1 --------------------+-----+--------------+-----------------------------+------------------------------+--------------- x4/3x4o3*a3/2o . ♦ 96 | 192 96 0 | 48 64 64 0 24 0 0 | 8 8 0 16 0 0 0 0 | 10 * * * * x4/3x4o3*a . x3*a ♦ 192 | 192 192 96 | 48 64 0 64 48 96 0 | 8 0 8 0 16 0 24 0 | * 10 * * * x4/3x . *a3/2o3x3*a ♦ 192 | 192 96 192 | 48 0 64 64 0 96 64 | 0 8 8 0 0 16 0 32 | * * 10 * * x . o3*a3/2o3x3*a ♦ 30 | 60 0 30 | 0 20 20 20 0 0 10 | 0 0 0 5 5 5 0 0 | * * * 32 * . x4o o3x ♦ 12 | 0 12 12 | 0 0 0 0 3 12 4 | 0 0 0 0 0 0 3 4 | * * * * 80
4/3
x---o
4/3 \ / 3/2
x
3 / \ 3/2
x---o
3
x4/3x4/3o3/2*a3/2o3x3*a . . . . . | 960 | 4 2 2 | 4 2 2 4 1 4 1 | 2 2 4 1 2 2 2 2 | 1 2 2 1 1 ------------------------+-----+--------------+-----------------------------+------------------------------+--------------- x . . . . | 2 | 1920 * * | 1 1 1 1 0 0 0 | 1 1 1 1 1 1 0 0 | 1 1 1 1 0 . x . . . | 2 | * 960 * | 2 0 0 0 1 2 0 | 2 1 2 0 0 0 2 1 | 1 2 1 0 1 . . . . x | 2 | * * 960 | 0 0 0 2 0 2 1 | 0 0 2 0 1 2 1 2 | 0 1 2 1 1 ------------------------+-----+--------------+-----------------------------+------------------------------+--------------- x4/3x . . . | 8 | 4 4 0 | 480 * * * * * * | 1 1 1 0 0 0 0 0 | 1 1 1 0 0 x . o3/2*a . . | 3 | 3 0 0 | * 640 * * * * * | 1 0 0 1 1 0 0 0 | 1 1 0 1 0 x . . *a3/2o . | 3 | 3 0 0 | * * 640 * * * * | 0 1 0 1 0 1 0 0 | 1 0 1 1 0 x . . . x3*a | 6 | 3 0 3 | * * * 640 * * * | 0 0 1 0 1 1 0 0 | 0 1 1 1 0 . x4/3o . . | 4 | 0 4 0 | * * * * 240 * * | 2 0 0 0 0 0 2 0 | 1 2 0 0 1 . x . . x | 4 | 0 2 2 | * * * * * 960 * | 0 0 1 0 0 0 1 1 | 0 1 1 0 1 . . . o3x | 3 | 0 0 3 | * * * * * * 320 | 0 0 0 0 0 2 0 2 | 0 0 2 1 1 ------------------------+-----+--------------+-----------------------------+------------------------------+--------------- x4/3x4/3o3/2*a . . ♦ 24 | 24 24 0 | 6 8 0 0 6 0 0 | 80 * * * * * * * | 1 1 0 0 0 x4/3x . *a3/2o . ♦ 24 | 24 12 0 | 6 0 8 0 0 0 0 | * 80 * * * * * * | 1 0 1 0 0 x4/3x . . x3*a ♦ 48 | 24 24 24 | 6 0 0 8 0 12 0 | * * 80 * * * * * | 0 1 1 0 0 x . o3/2*a3/2o . ♦ 6 | 12 0 0 | 0 4 4 0 0 0 0 | * * * 160 * * * * | 1 0 0 1 0 x . o3/2*a . x3*a ♦ 12 | 12 0 6 | 0 4 0 4 0 0 0 | * * * * 160 * * * | 0 1 0 1 0 x . . *a3/2o3x3*a ♦ 12 | 12 0 12 | 0 0 4 4 0 0 4 | * * * * * 160 * * | 0 0 1 1 0 . x4/3o . x ♦ 8 | 0 8 4 | 0 0 0 0 2 4 0 | * * * * * * 240 * | 0 1 0 0 1 . x . o3x ♦ 6 | 0 3 6 | 0 0 0 0 0 3 2 | * * * * * * * 320 | 0 0 1 0 1 ------------------------+-----+--------------+-----------------------------+------------------------------+--------------- x4/3x4/3o3/2*a3/2o . ♦ 96 | 192 96 0 | 48 64 64 0 24 0 0 | 8 8 0 16 0 0 0 0 | 10 * * * * x4/3x4/3o3/2*a . x3*a ♦ 192 | 192 192 96 | 48 64 0 64 48 96 0 | 8 0 8 0 16 0 24 0 | * 10 * * * x4/3x . *a3/2o3x3*a ♦ 192 | 192 96 192 | 48 0 64 64 0 96 64 | 0 8 8 0 0 16 0 32 | * * 10 * * x . o3/2*a3/2o3x3*a ♦ 30 | 60 0 30 | 0 20 20 20 0 0 10 | 0 0 0 5 5 5 0 0 | * * * 32 * . x4/3o o3x ♦ 12 | 0 12 12 | 0 0 0 0 3 12 4 | 0 0 0 0 0 0 3 4 | * * * * 80
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