©
wrt. pen
wrt. gittith
wrt. tes
©
| by facets: | gittith | pen | tepe | tes | tisdip |
| ginnont | 10 | 32 | 0 | 10 | 0 |
| gabdacan | 10 | 0 | 80 | 40 | 80 |
| quacant | 0 | 32 | 80 | 50 | 80 |
(at margins)
- general polytopal classes:
- Wythoffian polytera
- analogs:
- gocco series
links
| Acronym | ginnont | ||||||||||||||||||||||||
| Name | great penteractipenteractitriacontiditeron | ||||||||||||||||||||||||
| Field of sections |
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| Circumradius | sqrt[7-2 sqrt(2)]/2 = 1.021221 | ||||||||||||||||||||||||
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Inradius wrt. pen | [5-sqrt(2)]/sqrt(20) = 0.801806 | ||||||||||||||||||||||||
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Inradius wrt. gittith | 1/2 = 0.5 | ||||||||||||||||||||||||
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Inradius wrt. tes | (sqrt(2)-1)/2 = 0.207107 | ||||||||||||||||||||||||
| Vertex figure |
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| Coordinates | ((sqrt(2)-1)/2, 1/2, 1/2, 1/2, 1/2) & all permutations, all changes of sign | ||||||||||||||||||||||||
| Volume | [149 sqrt(2)-120]/30 = 3.023927 | ||||||||||||||||||||||||
| Surface | [-65+120 sqrt(2)+sqrt(5)]/3 = 35.647232 | ||||||||||||||||||||||||
| Colonel of regiment |
(is itself locally convex
– other uniform polyteral members:
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Dihedral angles
(at margins) | |||||||||||||||||||||||||
| Face vector | 160, 640, 640, 280, 52 | ||||||||||||||||||||||||
| Confer |
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External links |
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As abstract polytope ginnont is isomorphic to sinnont, thereby replacing octagrams by octagons, resp. gocco by socco and gittith by steth.
Incidence matrix according to Dynkin symbol
3 3 3
o---o---o---x
4 \ / 4/3
x
o3o3o3x4/3x4*c . . . . . | 160 | 4 4 | 6 6 4 | 4 4 6 | 1 1 4 ---------------+-----+---------+------------+-----------+--------- . . . x . | 2 | 320 * | 3 0 1 | 3 0 3 | 1 0 3 . . . . x | 2 | * 320 | 0 3 1 | 0 3 3 | 0 1 3 ---------------+-----+---------+------------+-----------+--------- . . o3x . | 3 | 3 0 | 320 * * | 2 0 1 | 1 0 2 . . o . x4*c | 4 | 0 4 | * 240 * | 0 2 1 | 0 1 2 . . . x4/3x | 8 | 4 4 | * * 80 | 0 0 3 | 0 0 3 ---------------+-----+---------+------------+-----------+--------- . o3o3x . ♦ 4 | 6 0 | 4 0 0 | 160 * * | 1 0 1 . o3o . x4*c ♦ 8 | 0 12 | 0 6 0 | * 80 * | 0 1 1 . . o3x4/3x4*c ♦ 24 | 24 24 | 8 6 6 | * * 40 | 0 0 2 ---------------+-----+---------+------------+-----------+--------- o3o3o3x . ♦ 5 | 10 0 | 10 0 0 | 5 0 0 | 32 * * o3o3o . x4*c ♦ 16 | 0 32 | 0 24 0 | 0 8 0 | * 10 * . o3o3x4/3x4*c ♦ 64 | 96 96 | 64 48 24 | 16 8 8 | * * 10
3 3 3/2
o---o---o---x
4/3 \ / 4/3
x
o3o3o3/2x4/3x4/3*c . . . . . | 160 | 4 4 | 6 6 4 | 4 4 6 | 1 1 4 -------------------+-----+---------+------------+-----------+--------- . . . x . | 2 | 320 * | 3 0 1 | 3 0 3 | 1 0 3 . . . . x | 2 | * 320 | 0 3 1 | 0 3 3 | 0 1 3 -------------------+-----+---------+------------+-----------+--------- . . o3/2x . | 3 | 3 0 | 320 * * | 2 0 1 | 1 0 2 . . o . x4/3*c | 4 | 0 4 | * 240 * | 0 2 1 | 0 1 2 . . . x4/3x | 8 | 4 4 | * * 80 | 0 0 3 | 0 0 3 -------------------+-----+---------+------------+-----------+--------- . o3o3/2x . ♦ 4 | 6 0 | 4 0 0 | 160 * * | 1 0 1 . o3o . x4/3*c ♦ 8 | 0 12 | 0 6 0 | * 80 * | 0 1 1 . . o3/2x4/3x4/3*c ♦ 24 | 24 24 | 8 6 6 | * * 40 | 0 0 2 -------------------+-----+---------+------------+-----------+--------- o3o3o3/2x . ♦ 5 | 10 0 | 10 0 0 | 5 0 0 | 32 * * o3o3o . x4/3*c ♦ 16 | 0 32 | 0 24 0 | 0 8 0 | * 10 * . o3o3/2x4/3x4/3*c ♦ 64 | 96 96 | 64 48 24 | 16 8 8 | * * 10
3 3/2 3
o---o---o---x
4 \ / 4/3
x
o3o3/2o3x4/3x4*c . . . . . | 160 | 4 4 | 6 6 4 | 4 4 6 | 1 1 4 -----------------+-----+---------+------------+-----------+--------- . . . x . | 2 | 320 * | 3 0 1 | 3 0 3 | 1 0 3 . . . . x | 2 | * 320 | 0 3 1 | 0 3 3 | 0 1 3 -----------------+-----+---------+------------+-----------+--------- . . o3x . | 3 | 3 0 | 320 * * | 2 0 1 | 1 0 2 . . o . x4*c | 4 | 0 4 | * 240 * | 0 2 1 | 0 1 2 . . . x4/3x | 8 | 4 4 | * * 80 | 0 0 3 | 0 0 3 -----------------+-----+---------+------------+-----------+--------- . o3/2o3x . ♦ 4 | 6 0 | 4 0 0 | 160 * * | 1 0 1 . o3/2o . x4*c ♦ 8 | 0 12 | 0 6 0 | * 80 * | 0 1 1 . . o3x4/3x4*c ♦ 24 | 24 24 | 8 6 6 | * * 40 | 0 0 2 -----------------+-----+---------+------------+-----------+--------- o3o3/2o3x . ♦ 5 | 10 0 | 10 0 0 | 5 0 0 | 32 * * o3o3/2o . x4*c ♦ 16 | 0 32 | 0 24 0 | 0 8 0 | * 10 * . o3/2o3x4/3x4*c ♦ 64 | 96 96 | 64 48 24 | 16 8 8 | * * 10
3 3/2 3/2
o---o---o---x
4/3 \ / 4/3
x
o3o3/2o3/2x4/3x4/3*c . . . . . | 160 | 4 4 | 6 6 4 | 4 4 6 | 1 1 4 ---------------------+-----+---------+------------+-----------+--------- . . . x . | 2 | 320 * | 3 0 1 | 3 0 3 | 1 0 3 . . . . x | 2 | * 320 | 0 3 1 | 0 3 3 | 0 1 3 ---------------------+-----+---------+------------+-----------+--------- . . o3/2x . | 3 | 3 0 | 320 * * | 2 0 1 | 1 0 2 . . o . x4/3*c | 4 | 0 4 | * 240 * | 0 2 1 | 0 1 2 . . . x4/3x | 8 | 4 4 | * * 80 | 0 0 3 | 0 0 3 ---------------------+-----+---------+------------+-----------+--------- . o3/2o3/2x . ♦ 4 | 6 0 | 4 0 0 | 160 * * | 1 0 1 . o3/2o . x4/3*c ♦ 8 | 0 12 | 0 6 0 | * 80 * | 0 1 1 . . o3/2x4/3x4/3*c ♦ 24 | 24 24 | 8 6 6 | * * 40 | 0 0 2 ---------------------+-----+---------+------------+-----------+--------- o3o3/2o3/2x . ♦ 5 | 10 0 | 10 0 0 | 5 0 0 | 32 * * o3o3/2o . x4/3*c ♦ 16 | 0 32 | 0 24 0 | 0 8 0 | * 10 * . o3/2o3/2x4/3x4/3*c ♦ 64 | 96 96 | 64 48 24 | 16 8 8 | * * 10
3/2 3 3
o---o---o---x
4 \ / 4/3
x
o3/2o3o3x4/3x4*c . . . . . | 160 | 4 4 | 6 6 4 | 4 4 6 | 1 1 4 -----------------+-----+---------+------------+-----------+--------- . . . x . | 2 | 320 * | 3 0 1 | 3 0 3 | 1 0 3 . . . . x | 2 | * 320 | 0 3 1 | 0 3 3 | 0 1 3 -----------------+-----+---------+------------+-----------+--------- . . o3x . | 3 | 3 0 | 320 * * | 2 0 1 | 1 0 2 . . o . x4*c | 4 | 0 4 | * 240 * | 0 2 1 | 0 1 2 . . . x4/3x | 8 | 4 4 | * * 80 | 0 0 3 | 0 0 3 -----------------+-----+---------+------------+-----------+--------- . o3o3x . ♦ 4 | 6 0 | 4 0 0 | 160 * * | 1 0 1 . o3o . x4*c ♦ 8 | 0 12 | 0 6 0 | * 80 * | 0 1 1 . . o3x4/3x4*c ♦ 24 | 24 24 | 8 6 6 | * * 40 | 0 0 2 -----------------+-----+---------+------------+-----------+--------- o3/2o3o3x . ♦ 5 | 10 0 | 10 0 0 | 5 0 0 | 32 * * o3/2o3o . x4*c ♦ 16 | 0 32 | 0 24 0 | 0 8 0 | * 10 * . o3o3x4/3x4*c ♦ 64 | 96 96 | 64 48 24 | 16 8 8 | * * 10
3/2 3 3/2
o---o---o---x
4/3 \ / 4/3
x
o3/2o3o3/2x4/3x4/3*c . . . . . | 160 | 4 4 | 6 6 4 | 4 4 6 | 1 1 4 ---------------------+-----+---------+------------+-----------+--------- . . . x . | 2 | 320 * | 3 0 1 | 3 0 3 | 1 0 3 . . . . x | 2 | * 320 | 0 3 1 | 0 3 3 | 0 1 3 ---------------------+-----+---------+------------+-----------+--------- . . o3/2x . | 3 | 3 0 | 320 * * | 2 0 1 | 1 0 2 . . o . x4/3*c | 4 | 0 4 | * 240 * | 0 2 1 | 0 1 2 . . . x4/3x | 8 | 4 4 | * * 80 | 0 0 3 | 0 0 3 ---------------------+-----+---------+------------+-----------+--------- . o3o3/2x . ♦ 4 | 6 0 | 4 0 0 | 160 * * | 1 0 1 . o3o . x4/3*c ♦ 8 | 0 12 | 0 6 0 | * 80 * | 0 1 1 . . o3/2x4/3x4/3*c ♦ 24 | 24 24 | 8 6 6 | * * 40 | 0 0 2 ---------------------+-----+---------+------------+-----------+--------- o3/2o3o3/2x . ♦ 5 | 10 0 | 10 0 0 | 5 0 0 | 32 * * o3/2o3o . x4/3*c ♦ 16 | 0 32 | 0 24 0 | 0 8 0 | * 10 * . o3o3/2x4/3x4/3*c ♦ 64 | 96 96 | 64 48 24 | 16 8 8 | * * 10
3/2 3/2 3
o---o---o---x
4 \ / 4/3
x
o3/2o3/2o3x4/3x4*c . . . . . | 160 | 4 4 | 6 6 4 | 4 4 6 | 1 1 4 -------------------+-----+---------+------------+-----------+--------- . . . x . | 2 | 320 * | 3 0 1 | 3 0 3 | 1 0 3 . . . . x | 2 | * 320 | 0 3 1 | 0 3 3 | 0 1 3 -------------------+-----+---------+------------+-----------+--------- . . o3x . | 3 | 3 0 | 320 * * | 2 0 1 | 1 0 2 . . o . x4*c | 4 | 0 4 | * 240 * | 0 2 1 | 0 1 2 . . . x4/3x | 8 | 4 4 | * * 80 | 0 0 3 | 0 0 3 -------------------+-----+---------+------------+-----------+--------- . o3/2o3x . ♦ 4 | 6 0 | 4 0 0 | 160 * * | 1 0 1 . o3/2o . x4*c ♦ 8 | 0 12 | 0 6 0 | * 80 * | 0 1 1 . . o3x4/3x4*c ♦ 24 | 24 24 | 8 6 6 | * * 40 | 0 0 2 -------------------+-----+---------+------------+-----------+--------- o3/2o3/2o3x . ♦ 5 | 10 0 | 10 0 0 | 5 0 0 | 32 * * o3/2o3/2o . x4*c ♦ 16 | 0 32 | 0 24 0 | 0 8 0 | * 10 * . o3/2o3x4/3x4*c ♦ 64 | 96 96 | 64 48 24 | 16 8 8 | * * 10
3/2 3/2 3/2
o---o---o---x
4/3 \ / 4/3
x
o3/2o3/2o3/2x4/3x4/3*c . . . . . | 160 | 4 4 | 6 6 4 | 4 4 6 | 1 1 4 -----------------------+-----+---------+------------+-----------+--------- . . . x . | 2 | 320 * | 3 0 1 | 3 0 3 | 1 0 3 . . . . x | 2 | * 320 | 0 3 1 | 0 3 3 | 0 1 3 -----------------------+-----+---------+------------+-----------+--------- . . o3/2x . | 3 | 3 0 | 320 * * | 2 0 1 | 1 0 2 . . o . x4/3*c | 4 | 0 4 | * 240 * | 0 2 1 | 0 1 2 . . . x4/3x | 8 | 4 4 | * * 80 | 0 0 3 | 0 0 3 -----------------------+-----+---------+------------+-----------+--------- . o3/2o3/2x . ♦ 4 | 6 0 | 4 0 0 | 160 * * | 1 0 1 . o3/2o . x4/3*c ♦ 8 | 0 12 | 0 6 0 | * 80 * | 0 1 1 . . o3/2x4/3x4/3*c ♦ 24 | 24 24 | 8 6 6 | * * 40 | 0 0 2 -----------------------+-----+---------+------------+-----------+--------- o3/2o3/2o3/2x . ♦ 5 | 10 0 | 10 0 0 | 5 0 0 | 32 * * o3/2o3/2o . x4/3*c ♦ 16 | 0 32 | 0 24 0 | 0 8 0 | * 10 * . o3/2o3/2x4/3x4/3*c ♦ 64 | 96 96 | 64 48 24 | 16 8 8 | * * 10
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