hexipentisteriruncicantitruncated octaexon,
omnitruncated octaexon,
permutoexon of 8 elements
wrt. toedip
wrt. hagippid
wrt. gocadip
wrt. gotaf
- general polytopal classes:
- Wythoffian polyexa
- analogs:
- omnitruncated simplex otSn
links
| Acronym | guph |
| Name |
great petated hexadecaexon, hexipentisteriruncicantitruncated octaexon, omnitruncated octaexon, permutoexon of 8 elements |
| Circumradius | sqrt(21) = 4.582576 |
|
Inradius wrt. toedip | 4 |
|
Inradius wrt. hagippid | sqrt(15) = 3.872983 |
|
Inradius wrt. gocadip | 2 sqrt(3) = 3.464102 |
|
Inradius wrt. gotaf | sqrt(7) = 2.645751 |
| Volume | 65536 |
| Face vector | 40320, 141120, 191520, 126000, 40824, 5796, 254 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x3x3x3x3x3x3x . . . . . . . | 40320 | 2 2 2 1 | 2 2 2 2 2 1 2 2 2 1 2 1 | 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 1 1 | 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1 2 2 2 1 | 2 2 2 2 2 2 2 2 1 2 1 1 | 2 2 2 1 -----------------+-------+-------------------------+-------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------+-------------------------------------------------+------------- x . . . . . . & | 2 | 40320 * * * | 1 1 1 1 1 1 0 0 0 0 0 0 | 1 1 1 1 2 1 1 1 2 1 1 1 1 0 0 0 0 0 0 | 1 1 1 2 1 1 2 1 2 1 1 1 2 1 1 1 0 0 0 | 1 1 2 1 2 2 1 2 1 1 1 0 | 1 2 2 1 . x . . . . . & | 2 | * 40320 * * | 1 0 0 0 1 0 1 1 1 1 0 0 | 1 1 1 2 1 0 0 1 0 0 1 0 1 1 1 2 1 1 0 | 1 1 2 1 1 2 1 2 1 1 0 1 0 1 0 1 1 2 1 | 1 2 1 2 1 2 2 1 1 1 0 1 | 2 1 2 1 . . x . . . . & | 2 | * * 40320 * | 0 1 0 1 0 0 1 0 1 0 1 1 | 1 0 1 0 0 1 2 1 1 1 0 0 1 1 2 1 1 0 1 | 1 2 1 1 1 0 0 1 1 0 2 1 1 2 1 1 2 1 1 | 2 1 1 2 2 1 1 1 0 2 1 1 | 2 2 1 1 . . . x . . . | 2 | * * * 20160 | 0 0 2 0 0 0 0 2 0 0 2 0 | 0 2 0 0 0 2 0 0 0 2 2 1 0 2 0 0 2 1 1 | 2 0 0 0 2 2 2 0 0 0 2 2 2 0 0 2 2 2 0 | 2 2 2 0 0 0 2 2 1 2 1 1 | 2 2 2 0 -----------------+-------+-------------------------+-------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------+-------------------------------------------------+------------- x3x . . . . . & | 6 | 3 3 0 0 | 13440 * * * * * * * * * * * | 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 | 1 1 1 1 1 2 1 1 1 0 0 0 | 1 1 2 1 x . x . . . . & | 4 | 2 0 2 0 | * 20160 * * * * * * * * * * | 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 | 1 1 1 1 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 | 1 1 1 1 2 1 0 1 0 1 1 0 | 1 2 1 1 x . . x . . . & | 4 | 2 0 0 2 | * * 20160 * * * * * * * * * | 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 | 1 0 0 0 1 1 2 0 0 0 1 1 2 0 0 1 0 0 0 | 1 1 2 0 0 0 1 2 1 1 1 0 | 1 2 2 0 x . . . x . . & | 4 | 2 0 2 0 | * * * 20160 * * * * * * * * | 0 0 1 0 0 0 1 0 1 1 0 0 1 0 0 0 0 0 0 | 0 1 0 1 1 0 0 1 1 0 1 0 1 1 1 1 0 0 0 | 1 0 1 1 2 1 1 1 0 1 1 0 | 1 2 1 1 x . . . . x . & | 4 | 2 2 0 0 | * * * * 20160 * * * * * * * | 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 | 0 0 1 1 0 1 1 1 1 1 0 1 0 1 0 1 0 0 0 | 0 1 1 1 1 2 1 1 1 1 0 0 | 1 1 2 1 x . . . . . x | 4 | 4 0 0 0 | * * * * * 10080 * * * * * * | 0 0 0 0 2 0 0 0 2 0 0 1 0 0 0 0 0 0 0 | 0 0 0 2 0 0 2 0 2 1 0 0 2 0 1 0 0 0 0 | 0 0 2 0 2 2 0 2 1 0 1 0 | 0 2 2 1 . x3x . . . . & | 6 | 0 3 3 0 | * * * * * * 13440 * * * * * | 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 | 1 1 1 1 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 | 1 1 1 2 1 1 1 0 0 1 0 1 | 2 1 1 1 . x . x . . . & | 4 | 0 2 0 2 | * * * * * * * 20160 * * * * | 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 | 1 0 0 0 1 2 1 0 0 0 0 1 0 0 0 1 1 2 0 | 1 2 1 0 0 0 2 1 1 1 0 1 | 2 1 2 0 . x . . x . . & | 4 | 0 2 2 0 | * * * * * * * * 20160 * * * | 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 | 0 1 1 0 1 0 0 1 1 0 0 1 0 1 0 0 1 1 1 | 1 1 0 2 1 1 1 1 0 1 0 1 | 2 1 1 1 . x . . . x . | 4 | 0 4 0 0 | * * * * * * * * * 10080 * * | 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 | 0 0 2 0 0 2 0 2 0 1 0 0 0 0 0 0 2 2 1 | 0 2 0 2 0 2 2 0 1 0 0 1 | 2 0 2 1 . . x3x . . . & | 6 | 0 0 3 3 | * * * * * * * * * * 13440 * | 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 | 1 0 0 0 1 0 0 0 0 0 2 1 1 0 0 1 2 1 0 | 2 1 1 1 0 0 1 1 0 2 1 1 | 2 2 1 0 . . x . x . . | 4 | 0 0 4 0 | * * * * * * * * * * * 10080 | 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 1 | 0 2 0 0 0 0 0 0 0 0 2 0 0 2 1 0 2 0 1 | 2 0 0 2 2 0 0 0 0 2 1 1 | 2 2 0 1 -----------------+-------+-------------------------+-------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------+-------------------------------------------------+------------- x3x3x . . . . & ♦ 24 | 12 12 12 0 | 4 6 0 0 0 0 4 0 0 0 0 0 | 3360 * * * * * * * * * * * * * * * * * * | 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 0 0 | 1 1 1 1 x3x . x . . . & ♦ 12 | 6 6 0 6 | 2 0 3 0 0 0 0 3 0 0 0 0 | * 6720 * * * * * * * * * * * * * * * * * | 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 1 1 1 0 0 0 | 1 1 2 0 x3x . . x . . & ♦ 12 | 6 6 6 0 | 2 0 0 3 0 0 0 0 3 0 0 0 | * * 6720 * * * * * * * * * * * * * * * * | 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 | 1 0 0 1 1 1 1 1 0 0 0 0 | 1 1 1 1 x3x . . . x . & ♦ 12 | 6 12 0 0 | 2 0 0 0 3 0 0 0 0 3 0 0 | * * * 6720 * * * * * * * * * * * * * * * | 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 | 0 1 0 1 0 2 1 0 1 0 0 0 | 1 0 2 1 x3x . . . . x & ♦ 12 | 12 6 0 0 | 2 0 0 0 3 3 0 0 0 0 0 0 | * * * * 6720 * * * * * * * * * * * * * * | 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 | 0 0 1 0 1 2 0 1 1 0 0 0 | 0 1 2 1 x . x3x . . . & ♦ 12 | 6 0 6 6 | 0 3 3 0 0 0 0 0 0 0 2 0 | * * * * * 6720 * * * * * * * * * * * * * | 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0 0 0 1 0 1 1 0 | 1 2 1 0 x . x . x . . & ♦ 8 | 4 0 8 0 | 0 2 0 2 0 0 0 0 0 0 0 2 | * * * * * * 10080 * * * * * * * * * * * * | 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 | 1 0 0 1 2 0 0 0 0 1 1 0 | 1 2 0 1 x . x . . x . & ♦ 8 | 4 4 4 0 | 0 2 0 0 2 0 0 0 2 0 0 0 | * * * * * * * 10080 * * * * * * * * * * * | 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 | 0 1 0 1 1 1 0 1 0 1 0 0 | 1 1 1 1 x . x . . . x & ♦ 8 | 8 0 4 0 | 0 2 0 2 0 2 0 0 0 0 0 0 | * * * * * * * * 10080 * * * * * * * * * * | 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 | 0 0 1 0 2 1 0 1 0 0 1 0 | 0 2 1 1 x . . x3x . . & ♦ 12 | 6 0 6 6 | 0 0 3 3 0 0 0 0 0 0 2 0 | * * * * * * * * * 6720 * * * * * * * * * | 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 | 1 0 1 0 0 0 1 1 0 1 1 0 | 1 2 1 0 x . . x . x . & ♦ 8 | 4 4 0 4 | 0 0 2 0 2 0 0 2 0 0 0 0 | * * * * * * * * * * 10080 * * * * * * * * | 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 | 0 1 1 0 0 0 1 1 1 1 0 0 | 1 1 2 0 x . . x . . x ♦ 8 | 8 0 0 4 | 0 0 4 0 0 2 0 0 0 0 0 0 | * * * * * * * * * * * 5040 * * * * * * * | 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 | 0 0 2 0 0 0 0 2 1 0 1 0 | 0 2 2 0 x . . . x3x . & ♦ 12 | 6 6 6 0 | 0 0 0 3 3 0 2 0 0 0 0 0 | * * * * * * * * * * * * 6720 * * * * * * | 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 | 0 0 1 1 1 1 1 0 0 1 0 0 | 1 1 1 1 . x3x3x . . . & ♦ 24 | 0 12 12 12 | 0 0 0 0 0 0 4 6 0 0 4 0 | * * * * * * * * * * * * * 3360 * * * * * | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 | 1 1 1 0 0 0 1 0 0 1 0 1 | 2 1 1 0 . x3x . x . . & ♦ 12 | 0 6 12 0 | 0 0 0 0 0 0 2 0 3 0 0 3 | * * * * * * * * * * * * * * 6720 * * * * | 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 | 1 0 0 2 1 0 0 0 0 1 0 1 | 2 1 0 1 . x3x . . x . & ♦ 12 | 0 12 6 0 | 0 0 0 0 0 0 2 0 3 3 0 0 | * * * * * * * * * * * * * * * 6720 * * * | 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 | 0 1 0 2 0 1 1 0 0 0 0 1 | 2 0 1 1 . x . x3x . . & ♦ 12 | 0 6 6 6 | 0 0 0 0 0 0 0 3 3 0 2 0 | * * * * * * * * * * * * * * * * 6720 * * | 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 | 1 1 0 0 0 0 1 1 0 1 0 1 | 2 1 1 0 . x . x . x . ♦ 8 | 0 8 0 4 | 0 0 0 0 0 0 0 4 0 2 0 0 | * * * * * * * * * * * * * * * * * 5040 * | 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 | 0 2 0 0 0 0 2 0 1 0 0 1 | 2 0 2 0 . . x3x3x . . ♦ 24 | 0 0 24 12 | 0 0 0 0 0 0 0 0 0 0 8 6 | * * * * * * * * * * * * * * * * * * 1680 | 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 | 2 0 0 0 0 0 0 0 0 2 1 1 | 2 2 0 0 -----------------+-------+-------------------------+-------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------+-------------------------------------------------+------------- x3x3x3x . . . & ♦ 120 | 60 60 60 60 | 20 30 30 0 0 0 20 30 0 0 20 0 | 5 10 0 0 0 10 0 0 0 0 0 0 0 5 0 0 0 0 0 | 672 * * * * * * * * * * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 | 1 1 1 0 x3x3x . x . . & ♦ 48 | 24 24 48 0 | 8 12 0 12 0 0 8 0 12 0 0 12 | 2 0 4 0 0 0 6 0 0 0 0 0 0 0 4 0 0 0 0 | * 1680 * * * * * * * * * * * * * * * * * | 1 0 0 1 1 0 0 0 0 0 0 0 | 1 1 0 1 x3x3x . . x . & ♦ 48 | 24 48 24 0 | 8 12 0 0 12 0 8 0 12 12 0 0 | 2 0 0 4 0 0 0 6 0 0 0 0 0 0 0 4 0 0 0 | * * 1680 * * * * * * * * * * * * * * * * | 0 1 0 1 0 1 0 0 0 0 0 0 | 1 0 1 1 x3x3x . . . x & ♦ 48 | 48 24 24 0 | 8 12 0 12 12 12 8 0 0 0 0 0 | 2 0 0 0 4 0 0 0 6 0 0 0 4 0 0 0 0 0 0 | * * * 1680 * * * * * * * * * * * * * * * | 0 0 1 0 1 1 0 0 0 0 0 0 | 0 1 1 1 x3x . x3x . . & ♦ 36 | 18 18 18 18 | 6 0 9 9 0 0 0 9 9 0 6 0 | 0 3 3 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 | * * * * 2240 * * * * * * * * * * * * * * | 1 0 0 0 0 0 1 1 0 0 0 0 | 1 1 1 0 x3x . x . x . & ♦ 24 | 12 24 0 12 | 4 0 6 0 6 0 0 12 0 6 0 0 | 0 2 0 2 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 | * * * * * 3360 * * * * * * * * * * * * * | 0 1 0 0 0 0 1 0 1 0 0 0 | 1 0 2 0 x3x . x . . x & ♦ 24 | 24 12 0 12 | 4 0 12 0 6 6 0 6 0 0 0 0 | 0 2 0 0 2 0 0 0 0 0 3 3 0 0 0 0 0 0 0 | * * * * * * 3360 * * * * * * * * * * * * | 0 0 1 0 0 0 0 1 1 0 0 0 | 0 1 2 0 x3x . . x3x . & ♦ 36 | 18 36 18 0 | 6 0 0 9 9 0 6 0 9 9 0 0 | 0 0 3 3 0 0 0 0 0 0 0 0 3 0 0 3 0 0 0 | * * * * * * * 2240 * * * * * * * * * * * | 0 0 0 1 0 1 1 0 0 0 0 0 | 1 0 1 1 x3x . . x . x & ♦ 24 | 24 12 12 0 | 4 6 0 6 6 6 0 0 6 0 0 0 | 0 0 2 0 2 0 0 3 3 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * 3360 * * * * * * * * * * | 0 0 0 0 1 1 0 1 0 0 0 0 | 0 1 1 1 x3x . . . x3x ♦ 36 | 36 36 0 0 | 12 0 0 0 18 9 0 0 0 9 0 0 | 0 0 0 6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * 1120 * * * * * * * * * | 0 0 0 0 0 2 0 0 1 0 0 0 | 0 0 2 1 x . x3x3x . . & ♦ 48 | 24 0 48 24 | 0 12 12 12 0 0 0 0 0 0 16 12 | 0 0 0 0 0 4 6 0 0 4 0 0 0 0 0 0 0 0 2 | * * * * * * * * * * 1680 * * * * * * * * | 1 0 0 0 0 0 0 0 0 1 1 0 | 1 2 0 0 x . x3x . x . & ♦ 24 | 12 12 12 12 | 0 6 6 0 6 0 0 6 6 0 4 0 | 0 0 0 0 0 2 0 3 0 0 3 0 0 0 0 0 2 0 0 | * * * * * * * * * * * 3360 * * * * * * * | 0 1 0 0 0 0 0 1 0 1 0 0 | 1 1 1 0 x . x3x . . x & ♦ 24 | 24 0 12 12 | 0 6 12 6 0 6 0 0 0 0 4 0 | 0 0 0 0 0 2 0 0 3 2 0 3 0 0 0 0 0 0 0 | * * * * * * * * * * * * 3360 * * * * * * | 0 0 1 0 0 0 0 1 0 0 1 0 | 0 2 1 0 x . x . x3x . & ♦ 24 | 12 12 24 0 | 0 6 0 6 6 0 4 0 6 0 0 6 | 0 0 0 0 0 0 3 3 0 0 0 0 2 0 2 0 0 0 0 | * * * * * * * * * * * * * 3360 * * * * * | 0 0 0 1 1 0 0 0 0 1 0 0 | 1 1 0 1 x . x . x . x ♦ 16 | 16 0 16 0 | 0 8 0 8 0 4 0 0 0 0 0 4 | 0 0 0 0 0 0 4 0 4 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * 2520 * * * * | 0 0 0 0 2 0 0 0 0 0 1 0 | 0 2 0 1 x . . x3x3x . & ♦ 48 | 24 24 24 24 | 0 0 12 12 12 0 8 12 0 0 8 0 | 0 0 0 0 0 0 0 0 0 4 6 0 4 2 0 0 0 0 0 | * * * * * * * * * * * * * * * 1680 * * * | 0 0 1 0 0 0 1 0 0 1 0 0 | 1 1 1 0 . x3x3x3x . . & ♦ 120 | 0 60 120 60 | 0 0 0 0 0 0 20 30 30 30 40 30 | 0 0 0 0 0 0 0 0 0 0 0 0 0 5 10 0 10 0 5 | * * * * * * * * * * * * * * * * 672 * * | 1 0 0 0 0 0 0 0 0 1 0 1 | 2 1 0 0 . x3x3x . x . & ♦ 48 | 0 48 24 24 | 0 0 0 0 0 0 8 24 12 12 8 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 4 4 6 0 | * * * * * * * * * * * * * * * * * 1680 * | 0 1 0 0 0 0 1 0 0 0 0 1 | 2 0 1 0 . x3x . x3x . ♦ 36 | 0 36 36 0 | 0 0 0 0 0 0 12 0 18 9 0 9 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 6 0 0 0 | * * * * * * * * * * * * * * * * * * 1120 | 0 0 0 2 0 0 0 0 0 0 0 1 | 2 0 0 1 -----------------+-------+-------------------------+-------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------+-------------------------------------------------+------------- x3x3x3x3x . . & ♦ 720 | 360 360 720 360 | 120 180 180 180 0 0 120 180 180 0 240 180 | 30 60 60 0 0 60 90 0 0 60 0 0 0 30 60 0 60 0 30 | 6 15 0 0 20 0 0 0 0 0 15 0 0 0 0 0 6 0 0 | 112 * * * * * * * * * * * | 1 1 0 0 x3x3x3x . x . & ♦ 240 | 120 240 120 120 | 40 60 60 0 60 0 40 120 60 60 40 0 | 10 20 0 20 0 20 0 30 0 0 30 0 0 10 0 20 20 30 0 | 2 0 5 0 0 10 0 0 0 0 0 10 0 0 0 0 0 5 0 | * 336 * * * * * * * * * * | 1 0 1 0 x3x3x3x . . x & ♦ 240 | 240 120 120 120 | 40 60 120 60 60 60 40 60 0 0 40 0 | 10 20 0 0 20 20 0 0 30 20 30 30 20 10 0 0 0 0 0 | 2 0 0 5 0 0 10 0 0 0 0 0 10 0 0 5 0 0 0 | * * 336 * * * * * * * * * | 0 1 1 0 x3x3x . x3x . & ♦ 144 | 72 144 144 0 | 24 36 0 36 36 0 48 0 72 36 24 36 | 6 0 12 12 0 0 18 18 0 0 0 0 12 0 24 24 0 0 0 | 0 3 3 0 0 0 0 4 0 0 0 0 0 6 0 0 0 0 4 | * * * 560 * * * * * * * * | 1 0 0 1 x3x3x . x . x & ♦ 96 | 96 48 96 0 | 16 48 0 48 24 24 16 0 24 0 0 24 | 4 0 8 0 8 0 24 12 24 0 0 0 8 0 8 0 0 0 0 | 0 2 0 2 0 0 0 0 4 0 0 0 0 4 6 0 0 0 0 | * * * * 840 * * * * * * * | 0 1 0 1 x3x3x . . x3x & ♦ 144 | 144 144 72 0 | 48 36 0 36 72 36 24 0 36 36 0 0 | 6 0 12 24 24 0 0 18 18 0 0 0 12 0 0 12 0 0 0 | 0 0 3 3 0 0 0 4 6 4 0 0 0 0 0 0 0 0 0 | * * * * * 560 * * * * * * | 0 0 1 1 x3x . x3x3x . & ♦ 144 | 72 144 72 72 | 24 0 36 36 36 0 24 72 36 36 24 0 | 0 12 12 12 0 0 0 0 0 12 18 0 12 6 0 12 12 18 0 | 0 0 0 0 4 6 0 4 0 0 0 0 0 0 0 3 0 3 0 | * * * * * * 560 * * * * * | 1 0 1 0 x3x . x3x . x & ♦ 72 | 72 36 36 36 | 12 18 36 18 18 18 0 18 18 0 12 0 | 0 6 6 0 6 6 0 9 9 6 9 9 0 0 0 0 6 0 0 | 0 0 0 0 2 0 3 0 3 0 0 3 3 0 0 0 0 0 0 | * * * * * * * 1120 * * * * | 0 1 1 0 x3x . x . x3x ♦ 72 | 72 72 0 36 | 24 0 36 0 36 18 0 36 0 18 0 0 | 0 12 0 12 12 0 0 0 0 0 18 9 0 0 0 0 0 9 0 | 0 0 0 0 0 6 6 0 0 2 0 0 0 0 0 0 0 0 0 | * * * * * * * * 560 * * * | 0 0 2 0 x . x3x3x3x . & ♦ 240 | 120 120 240 120 | 0 60 60 60 60 0 40 60 60 0 80 60 | 0 0 0 0 0 20 30 30 0 20 30 0 20 10 20 0 20 0 10 | 0 0 0 0 0 0 0 0 0 0 5 10 0 10 0 5 2 0 0 | * * * * * * * * * 336 * * | 1 1 0 0 x . x3x3x . x ♦ 96 | 96 0 96 48 | 0 48 48 48 0 24 0 0 0 0 32 24 | 0 0 0 0 0 16 24 0 24 16 0 12 0 0 0 0 0 0 4 | 0 0 0 0 0 0 0 0 0 0 4 0 8 0 6 0 0 0 0 | * * * * * * * * * * 420 * | 0 2 0 0 . x3x3x3x3x . ♦ 720 | 0 720 720 360 | 0 0 0 0 0 0 240 360 360 180 240 180 | 0 0 0 0 0 0 0 0 0 0 0 0 0 60 120 120 120 90 30 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 30 20 | * * * * * * * * * * * 56 | 2 0 0 0 -----------------+-------+-------------------------+-------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------+-------------------------------------------------+------------- x3x3x3x3x3x . & ♦ 5040 | 2520 5040 5040 2520 | 840 1260 1260 1260 1260 0 1680 2520 2520 1260 1680 1260 | 210 420 420 420 0 420 630 630 0 420 630 0 420 420 840 840 840 630 210 | 42 105 105 0 140 210 0 140 0 0 105 210 0 210 0 105 84 210 140 | 7 21 0 35 0 0 35 0 0 21 0 7 | 16 * * * x3x3x3x3x . x & ♦ 1440 | 1440 720 1440 720 | 240 720 720 720 360 360 240 360 360 0 480 360 | 60 120 120 0 120 240 360 180 360 240 180 180 120 60 120 0 120 0 60 | 12 30 0 30 40 0 60 0 60 0 60 60 120 60 90 30 12 0 0 | 2 0 6 0 15 0 0 20 0 6 15 0 | * 56 * * x3x3x3x . x3x & ♦ 720 | 720 720 360 360 | 240 180 360 180 360 180 120 360 180 180 120 0 | 30 120 60 120 120 60 0 90 90 60 180 90 60 30 0 60 60 90 0 | 6 0 15 15 20 60 60 20 30 20 0 30 30 0 0 15 0 15 0 | 0 3 3 0 0 5 5 10 10 0 0 0 | * * 112 * x3x3x . x3x3x ♦ 576 | 576 576 576 0 | 192 288 0 288 288 144 192 0 288 144 0 144 | 48 0 96 96 96 0 144 144 144 0 0 0 96 0 96 96 0 0 0 | 0 24 24 24 0 0 0 32 48 16 0 0 0 48 36 0 0 0 16 | 0 0 0 8 12 8 0 0 0 0 0 0 | * * * 70
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