fro

Acronym	fro
Name	facetorectified octeract
Circumradius	sqrt(7/2) = 1.870829
Inradius wrt. oca	-7/4 = -1.75
Inradius wrt. toc	5/4 = 1.25
Inradius wrt. bittoc	-3/4 = -0.75
Inradius wrt. tattoc	1/4 = 0.25
Coordinates	(1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0) & all permutations, all changes of sign
Surface	4096
General of army	recto
Colonel of regiment	recto
Dihedral angles (at margins)	at batal between bittoc and tattoc: arccos(3/4) = 41.409622° at fe between tattoc and tattoc: arccos(3/4) = 41.409622° at hop between oca and toc: arccos(3/4) = 41.409622° at til between bittoc and toc: arccos(3/4) = 41.409622°
Face vector	1024, 7168, 21504, 35840, 35840, 21504, 7168, 1024
Confer	general polytopal classes: Wythoffian polyzetta analogs: facetorectified hypercube frC_n

Fro has frasas for pseudo facets.

Incidence matrix according to Dynkin symbol

x3x3o3o3o3o3o3o3/2*a

. . . . . . . .        | 1024 |   14 |   42    42 |   210    70 |   280  210    70 |  210  420   42 |   84  210  140   14 |  14  42  70   2
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x . . . . . . .      & |    2 | 7168 |    6     6 |    45    15 |    80   60    20 |   75  150   15 |   36   90   60    6 |   7  21  35   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x . . . . . .        |    6 |    6 | 7168     * |    10     0 |    20   20     0 |   20   60    0 |   10   40   30    0 |   2  10  20   0
x . . . . . . o3/2*a & |    3 |    3 |    * 14336 |     5     5 |    20   10    10 |   30   40   10 |   20   35   20    5 |   5  11  15   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x3o . . . . .      & ♦   12 |   18 |    4     4 | 17920     * |     4    4     0 |    6   18    0 |    4   16   12    0 |   1   5  10   0
x . . . . . o3o3/2*a & ♦    4 |    6 |    0     4 |     * 17920 |     4    0     4 |   12    6    6 |   12   12    4    4 |   4   6   5   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x3o3o . . . .      & ♦   20 |   40 |   10    20 |     5     5 | 14336    *     * |    3    3    0 |    3    6    3    0 |   1   3   4   0
x3x3o . . . . o3/2*a   ♦   30 |   60 |   20    20 |    10     0 |     * 7168     * |    0    6    0 |    0    6    6    0 |   0   2   6   0
x . . . . o3o3o3/2*a & ♦    5 |   10 |    0    10 |     0     5 |     *    * 14336 |    3    0    3 |    6    3    0    3 |   3   3   1   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x3o3o3o . . .      & ♦   30 |   75 |   20    60 |    15    30 |     6    0     6 | 7168    *    * |    2    2    0    0 |   1   2   1   0
x3x3o3o . . . o3/2*a & ♦   60 |  150 |   60    80 |    45    15 |     6    6     0 |    * 7168    * |    0    2    2    0 |   0   1   3   0
x . . . o3o3o3o3/2*a & ♦    6 |   15 |    0    20 |     0    15 |     0    0     6 |    *    * 7168 |    2    0    0    2 |   2   1   0   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x3o3o3o3o . .      & ♦   42 |  126 |   35   140 |    35   105 |    21    0    42 |    7    0    7 | 2048    *    *    * |   1   1   0   0
x3x3o3o3o . . o3/2*a & ♦  105 |  315 |  140   245 |   140   105 |    42   21    21 |    7    7    0 |    * 2048    *    * |   0   1   1   0
x3x3o3o . . o3o3/2*a   ♦  140 |  420 |  210   280 |   210    70 |    42   42     0 |    0   14    0 |    *    * 1024    * |   0   0   2   0
x . . o3o3o3o3o3/2*a & ♦    7 |   21 |    0    35 |     0    35 |     0    0    21 |    0    0    7 |    *    *    * 2048 |   1   0   0   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x3o3o3o3o3o .      & ♦   56 |  196 |   56   280 |    70   280 |    56    0   168 |   28    0   56 |    8    0    0    8 | 256   *   *   *
x3x3o3o3o3o . o3/2*a & ♦  168 |  588 |  280   616 |   350   420 |   168   56   168 |   56   28   28 |    8    8    0    0 |   * 256   *   *
x3x3o3o3o . o3o3/2*a & ♦  280 |  980 |  560   840 |   700   350 |   224  168    56 |   28   84    0 |    0    8    8    0 |   *   * 256   *
x . o3o3o3o3o3o3/2*a & ♦    8 |   28 |    0    56 |     0    70 |     0    0    56 |    0    0   28 |    0    0    0    8 |   *   *   * 256

x3x3o3o3o3o3o3/2o3*a

. . . . . . .   .      | 1024 |   14 |   42    42 |   210    70 |   280  210    70 |  210  420   42 |   84  210  140   14 |  14  42  70   2
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x . . . . . .   .    & |    2 | 7168 |    6     6 |    45    15 |    80   60    20 |   75  150   15 |   36   90   60    6 |   7  21  35   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x . . . . .   .      |    6 |    6 | 7168     * |    10     0 |    20   20     0 |   20   60    0 |   10   40   30    0 |   2  10  20   0
x . . . . . .   o3*a & |    3 |    3 |    * 14336 |     5     5 |    20   10    10 |   30   40   10 |   20   35   20    5 |   5  11  15   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x3o . . . . .      & ♦   12 |   18 |    4     4 | 17920     * |     4    4     0 |    6   18    0 |    4   16   12    0 |   1   5  10   0
x . . . . . o3/2o3*a & ♦    4 |    6 |    0     4 |     * 17920 |     4    0     4 |   12    6    6 |   12   12    4    4 |   4   6   5   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x3o3o . . .   .    & ♦   20 |   40 |   10    20 |     5     5 | 14336    *     * |    3    3    0 |    3    6    3    0 |   1   3   4   0
x3x3o . . . .   o3*a   ♦   30 |   60 |   20    20 |    10     0 |     * 7168     * |    0    6    0 |    0    6    6    0 |   0   2   6   0
x . . . . o3o3/2o3*a & ♦    5 |   10 |    0    10 |     0     5 |     *    * 14336 |    3    0    3 |    6    3    0    3 |   3   3   1   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x3o3o3o . .   .    & ♦   30 |   75 |   20    60 |    15    30 |     6    0     6 | 7168    *    * |    2    2    0    0 |   1   2   1   0
x3x3o3o . . .   o3*a & ♦   60 |  150 |   60    80 |    45    15 |     6    6     0 |    * 7168    * |    0    2    2    0 |   0   1   3   0
x . . . o3o3o3/2o3*a & ♦    6 |   15 |    0    20 |     0    15 |     0    0     6 |    *    * 7168 |    2    0    0    2 |   2   1   0   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x3o3o3o3o .   .    & ♦   42 |  126 |   35   140 |    35   105 |    21    0    42 |    7    0    7 | 2048    *    *    * |   1   1   0   0
x3x3o3o3o . .   o3*a & ♦  105 |  315 |  140   245 |   140   105 |    42   21    21 |    7    7    0 |    * 2048    *    * |   0   1   1   0
x3x3o3o . . o3/2o3*a   ♦  140 |  420 |  210   280 |   210    70 |    42   42     0 |    0   14    0 |    *    * 1024    * |   0   0   2   0
x . . o3o3o3o3/2o3*a & ♦    7 |   21 |    0    35 |     0    35 |     0    0    21 |    0    0    7 |    *    *    * 2048 |   1   0   0   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x3o3o3o3o3o   .    & ♦   56 |  196 |   56   280 |    70   280 |    56    0   168 |   28    0   56 |    8    0    0    8 | 256   *   *   *
x3x3o3o3o3o .   o3*a & ♦  168 |  588 |  280   616 |   350   420 |   168   56   168 |   56   28   28 |    8    8    0    0 |   * 256   *   *
x3x3o3o3o . o3/2o3*a & ♦  280 |  980 |  560   840 |   700   350 |   224  168    56 |   28   84    0 |    0    8    8    0 |   *   * 256   *
x . o3o3o3o3o3/2o3*a & ♦    8 |   28 |    0    56 |     0    70 |     0    0    56 |    0    0   28 |    0    0    0    8 |   *   *   * 256

x3x3o3o3o3o3/2o3o3*a

. . . . . .   . .      | 1024 |   14 |   42    42 |   210    70 |   280  210    70 |  210  420   42 |   84  210  140   14 |  14  42  70   2
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x . . . . .   . .    & |    2 | 7168 |    6     6 |    45    15 |    80   60    20 |   75  150   15 |   36   90   60    6 |   7  21  35   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x . . . .   . .      |    6 |    6 | 7168     * |    10     0 |    20   20     0 |   20   60    0 |   10   40   30    0 |   2  10  20   0
x . . . . .   . o3*a & |    3 |    3 |    * 14336 |     5     5 |    20   10    10 |   30   40   10 |   20   35   20    5 |   5  11  15   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x3o . . .   . .    & ♦   12 |   18 |    4     4 | 17920     * |     4    4     0 |    6   18    0 |    4   16   12    0 |   1   5  10   0
x . . . . .   o3o3*a & ♦    4 |    6 |    0     4 |     * 17920 |     4    0     4 |   12    6    6 |   12   12    4    4 |   4   6   5   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x3o3o . .   . .    & ♦   20 |   40 |   10    20 |     5     5 | 14336    *     * |    3    3    0 |    3    6    3    0 |   1   3   4   0
x3x3o . . .   . o3*a   ♦   30 |   60 |   20    20 |    10     0 |     * 7168     * |    0    6    0 |    0    6    6    0 |   0   2   6   0
x . . . . o3/2o3o3*a & ♦    5 |   10 |    0    10 |     0     5 |     *    * 14336 |    3    0    3 |    6    3    0    3 |   3   3   1   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x3o3o3o .   . .    & ♦   30 |   75 |   20    60 |    15    30 |     6    0     6 | 7168    *    * |    2    2    0    0 |   1   2   1   0
x3x3o3o . .   . o3*a & ♦   60 |  150 |   60    80 |    45    15 |     6    6     0 |    * 7168    * |    0    2    2    0 |   0   1   3   0
x . . . o3o3/2o3o3*a & ♦    6 |   15 |    0    20 |     0    15 |     0    0     6 |    *    * 7168 |    2    0    0    2 |   2   1   0   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x3o3o3o3o   . .    & ♦   42 |  126 |   35   140 |    35   105 |    21    0    42 |    7    0    7 | 2048    *    *    * |   1   1   0   0
x3x3o3o3o .   . o3*a & ♦  105 |  315 |  140   245 |   140   105 |    42   21    21 |    7    7    0 |    * 2048    *    * |   0   1   1   0
x3x3o3o . .   o3o3*a   ♦  140 |  420 |  210   280 |   210    70 |    42   42     0 |    0   14    0 |    *    * 1024    * |   0   0   2   0
x . . o3o3o3/2o3o3*a & ♦    7 |   21 |    0    35 |     0    35 |     0    0    21 |    0    0    7 |    *    *    * 2048 |   1   0   0   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x3o3o3o3o3/2o .    & ♦   56 |  196 |   56   280 |    70   280 |    56    0   168 |   28    0   56 |    8    0    0    8 | 256   *   *   *
x3x3o3o3o3o   . o3*a & ♦  168 |  588 |  280   616 |   350   420 |   168   56   168 |   56   28   28 |    8    8    0    0 |   * 256   *   *
x3x3o3o3o .   o3o3*a & ♦  280 |  980 |  560   840 |   700   350 |   224  168    56 |   28   84    0 |    0    8    8    0 |   *   * 256   *
x . o3o3o3o3/2o3o3*a & ♦    8 |   28 |    0    56 |     0    70 |     0    0    56 |    0    0   28 |    0    0    0    8 |   *   *   * 256

x3x3o3o3o3/2o3o3o3*a

. . . . .   . . .      | 1024 |   14 |   42    42 |   210    70 |   280  210    70 |  210  420   42 |   84  210  140   14 |  14  42  70   2
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x . . . .   . . .    & |    2 | 7168 |    6     6 |    45    15 |    80   60    20 |   75  150   15 |   36   90   60    6 |   7  21  35   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x . . .   . . .      |    6 |    6 | 7168     * |    10     0 |    20   20     0 |   20   60    0 |   10   40   30    0 |   2  10  20   0
x . . . .   . . o3*a & |    3 |    3 |    * 14336 |     5     5 |    20   10    10 |   30   40   10 |   20   35   20    5 |   5  11  15   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x3o . .   . . .    & ♦   12 |   18 |    4     4 | 17920     * |     4    4     0 |    6   18    0 |    4   16   12    0 |   1   5  10   0
x . . . .   . o3o3*a & ♦    4 |    6 |    0     4 |     * 17920 |     4    0     4 |   12    6    6 |   12   12    4    4 |   4   6   5   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x3o3o .   . . .    & ♦   20 |   40 |   10    20 |     5     5 | 14336    *     * |    3    3    0 |    3    6    3    0 |   1   3   4   0
x3x3o . .   . . o3*a   ♦   30 |   60 |   20    20 |    10     0 |     * 7168     * |    0    6    0 |    0    6    6    0 |   0   2   6   0
x . . . .   o3o3o3*a & ♦    5 |   10 |    0    10 |     0     5 |     *    * 14336 |    3    0    3 |    6    3    0    3 |   3   3   1   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x3o3o3o   . . .    & ♦   30 |   75 |   20    60 |    15    30 |     6    0     6 | 7168    *    * |    2    2    0    0 |   1   2   1   0
x3x3o3o .   . . o3*a & ♦   60 |  150 |   60    80 |    45    15 |     6    6     0 |    * 7168    * |    0    2    2    0 |   0   1   3   0
x . . . o3/2o3o3o3*a & ♦    6 |   15 |    0    20 |     0    15 |     0    0     6 |    *    * 7168 |    2    0    0    2 |   2   1   0   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x3o3o3o3/2o . .    & ♦   42 |  126 |   35   140 |    35   105 |    21    0    42 |    7    0    7 | 2048    *    *    * |   1   1   0   0
x3x3o3o3o   . . o3*a & ♦  105 |  315 |  140   245 |   140   105 |    42   21    21 |    7    7    0 |    * 2048    *    * |   0   1   1   0
x3x3o3o .   . o3o3*a   ♦  140 |  420 |  210   280 |   210    70 |    42   42     0 |    0   14    0 |    *    * 1024    * |   0   0   2   0
x . . o3o3/2o3o3o3*a & ♦    7 |   21 |    0    35 |     0    35 |     0    0    21 |    0    0    7 |    *    *    * 2048 |   1   0   0   1
-----------------------+------+------+------------+-------------+------------------+----------------+---------------------+----------------
x3x3o3o3o3/2o3o .    & ♦   56 |  196 |   56   280 |    70   280 |    56    0   168 |   28    0   56 |    8    0    0    8 | 256   *   *   *
x3x3o3o3o3/2o . o3*a & ♦  168 |  588 |  280   616 |   350   420 |   168   56   168 |   56   28   28 |    8    8    0    0 |   * 256   *   *
x3x3o3o3o   . o3o3*a & ♦  280 |  980 |  560   840 |   700   350 |   224  168    56 |   28   84    0 |    0    8    8    0 |   *   * 256   *
x . o3o3o3/2o3o3o3*a & ♦    8 |   28 |    0    56 |     0    70 |     0    0    56 |    0    0   28 |    0    0    0    8 |   *   *   * 256

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