Acronym brene
Name birectified enneazetton,
Gosset polytope 05,2
Circumradius 1
Inradius
wrt. roc 		1/2 = 0.5
Inradius
wrt. broc 		1/4 = 0.25
Volume 1431/71680 = 0.019964
Surface 1311/2240 = 0.585268
Dihedral angles
(at margins)
  • at ril between broc and roc:   arccos(-1/8) = 97.180756°
  • at hop between roc and roc:   arccos(1/8) = 82.819244°
  • at bril between broc and broc:   arccos(1/8) = 82.819244°
Face vector 84, 756, 1764, 2016, 1386, 588, 144, 18
Confer
uniform relative:
fy  
general polytopal classes:
Wythoffian polyzetta   segmentozetta   fundamental lace prisms   Coxeter-Elte-Gosset polytopes  
analogs:
birectified simplex brSn  
External
links 		wikipedia   polytopewiki

Incidence matrix according to Dynkin symbol

o3o3x3o3o3o3o3o

. . . . . . . . | 84 ♦  18 |  18   45 |   6  45   60 |  15  60  45 | 20  45  18 | 15 18  3 | 6 3
----------------+----+-----+----------+--------------+-------------+------------+----------+----
. . x . . . . . |  2 | 756 |   2    5 |   1  10   10 |   5  20  10 | 10  20   5 | 10 10  1 | 5 2
----------------+----+-----+----------+--------------+-------------+------------+----------+----
. o3x . . . . . |  3 |   3 | 504    * |   1   5    0 |   5  10   0 | 10  10   0 | 10  5  0 | 5 1
. . x3o . . . . |  3 |   3 |   * 1260 |   0   2    4 |   1   8   6 |  6  12   4 |  6  8  1 | 4 2
----------------+----+-----+----------+--------------+-------------+------------+----------+----
o3o3x . . . . . ♦  4 |   6 |   4    0 | 126   *    * ♦   5   0   0 | 10   0   0 | 10  0  0 | 5 0
. o3x3o . . . . ♦  6 |  12 |   4    4 |   * 630    * |   1   4   0 |  4   6   0 |  6  4  0 | 4 1
. . x3o3o . . . ♦  4 |   6 |   0    4 |   *   * 1260 |   0   2   3 |  1   6   3 |  3  6  1 | 3 2
----------------+----+-----+----------+--------------+-------------+------------+----------+----
o3o3x3o . . . . ♦ 10 |  30 |  20   10 |   5   5    0 | 126   *   * ♦  4   0   0 |  6  0  0 | 4 0
. o3x3o3o . . . ♦ 10 |  30 |  10   20 |   0   5    5 |   * 504   * |  1   3   0 |  3  3  0 | 3 1
. . x3o3o3o . . ♦  5 |  10 |   0   10 |   0   0    5 |   *   * 756 |  0   2   2 |  1  4  1 | 2 2
----------------+----+-----+----------+--------------+-------------+------------+----------+----
o3o3x3o3o . . . ♦ 20 |  90 |  60   60 |  15  30   15 |   6   6   0 | 84   *   * |  3  0  0 | 3 0
. o3x3o3o3o . . ♦ 15 |  60 |  20   60 |   0  15   30 |   0   6   6 |  * 252   * |  1  2  0 | 2 1
. . x3o3o3o3o . ♦  6 |  15 |   0   20 |   0   0   15 |   0   0   6 |  *   * 252 |  0  2  1 | 1 2
----------------+----+-----+----------+--------------+-------------+------------+----------+----
o3o3x3o3o3o . . ♦ 35 | 210 | 140  210 |  35 105  105 |  21  42  21 |  7   7   0 | 36  *  * | 2 0
. o3x3o3o3o3o . ♦ 21 | 105 |  35  140 |   0  35  105 |   0  21  42 |  0   7   7 |  * 72  * | 1 1
. . x3o3o3o3o3o ♦  7 |  21 |   0   35 |   0   0   35 |   0   0  21 |  0   0   7 |  *  * 36 | 0 2
----------------+----+-----+----------+--------------+-------------+------------+----------+----
o3o3x3o3o3o3o . ♦ 56 | 420 | 280  560 |  70 280  420 |  56 168 168 | 28  56  28 |  8  8  0 | 9 *
. o3x3o3o3o3o3o ♦ 28 | 168 |  56  280 |   0  70  280 |   0  56 168 |  0  28  56 |  0  8  8 | * 9


oo3xo3ox3oo3oo3oo3oo&#x   → height = 3/4
(roc || broc)

o.3o.3o.3o.3o.3o.3o.    | 28  * ♦  12   6   0 |  6  30  12  15   0   0 | 15  40  6  30  20  0   0   0 | 20  30 15  40  15  0   0   0 | 15 12 20  30   6  0  0  0 | 6 2 15 12  1 0 0 | 1 6 2 0
.o3.o3.o3.o3.o3.o3.o    |  * 56 ♦   0   3  15 |  0   0   3  15  15  30 |  0   0  1  15  30  5  30  30 |  0   0  5  30  30 10  30  15 |  0  0 10  30  15 10 15  3 | 0 0 10 15  3 5 3 | 0 5 3 1
------------------------+-------+-------------+------------------------+------------------------------+------------------------------+---------------------------+------------------+--------
.. x. .. .. .. .. ..    |  2  0 | 168   *   * |  1   5   1   0   0   0 |  5  10  1   5   0  0   0   0 | 10  10  5  10   0  0   0   0 | 10  5 10  10   0  0  0  0 | 5 1 10  5  0 0 0 | 1 5 1 0
oo3oo3oo3oo3oo3oo3oo&#x |  1  1 |   * 168   * |  0   0   2   5   0   0 |  0   0  1  10  10  0   0   0 |  0   0  5  20  10  0   0   0 |  0  0 10  20   5  0  0  0 | 0 0 10 10  1 0 0 | 0 5 2 0
.. .. .x .. .. .. ..    |  0  2 |   *   * 420 |  0   0   0   1   2   4 |  0   0  0   2   4  1   8   6 |  0   0  1   8   6  4  12   4 |  0  0  4  12   4  6  8  1 | 0 0  6  8  1 4 2 | 0 4 2 1
------------------------+-------+-------------+------------------------+------------------------------+------------------------------+---------------------------+------------------+--------
o.3x. .. .. .. .. ..    |  3  0 |   3   0   0 | 56   *   *   *   *   * |  5   0  1   0   0  0   0   0 | 10   0  5   0   0  0   0   0 | 10  0 10   0   0  0  0  0 | 5 0 10  0  0 0 0 | 1 5 0 0
.. x.3o. .. .. .. ..    |  3  0 |   3   0   0 |  * 280   *   *   *   * |  1   4  0   1   0  0   0   0 |  4   6  1   4   0  0   0   0 |  6  4  4   6   0  0  0  0 | 4 1  6  4  0 0 0 | 1 4 1 0
.. xo .. .. .. .. ..&#x |  2  1 |   1   2   0 |  *   * 168   *   *   * |  0   0  1   5   0  0   0   0 |  0   0  5  10   0  0   0   0 |  0  0 10  10   0  0  0  0 | 0 0 10  5  0 0 0 | 0 5 1 0
.. .. ox .. .. .. ..&#x |  1  2 |   0   2   1 |  *   *   * 420   *   * |  0   0  0   2   4  0   0   0 |  0   0  1   8   6  0   0   0 |  0  0  4  12   4  0  0  0 | 0 0  6  8  1 0 0 | 0 4 2 0
.. .o3.x .. .. .. ..    |  0  3 |   0   0   3 |  *   *   *   * 280   * |  0   0  0   1   0  1   4   0 |  0   0  1   4   0  4   6   0 |  0  0  4   6   0  6  4  0 | 0 0  6  4  0 4 1 | 0 4 1 1
.. .. .x3.o .. .. ..    |  0  3 |   0   0   3 |  *   *   *   *   * 560 |  0   0  0   0   1  0   2   3 |  0   0  0   2   3  1   6   3 |  0  0  1   6   3  3  6  1 | 0 0  3  6  1 3 2 | 0 3 2 1
------------------------+-------+-------------+------------------------+------------------------------+------------------------------+---------------------------+------------------+--------
o.3x.3o. .. .. .. ..    ♦  6  0 |  12   0   0 |  4   4   0   0   0   0 | 70   *  *   *   *  *   *   * |  4   0  1   0   0  0   0   0 |  6  0  4   0   0  0  0  0 | 4 0  6  0  0 0 0 | 1 4 0 0
.. x.3o.3o. .. .. ..    ♦  4  0 |   6   0   0 |  0   4   0   0   0   0 |  * 280  *   *   *  *   *   * |  1   3  0   1   0  0   0   0 |  3  3  1   3   0  0  0  0 | 3 1  3  3  0 0 0 | 1 3 1 0
oo3xo .. .. .. .. ..&#x ♦  3  1 |   3   3   0 |  1   0   3   0   0   0 |  *   * 56   *   *  *   *   * ♦  0   0  5   0   0  0   0   0 |  0  0 10   0   0  0  0  0 | 0 0 10  0  0 0 0 | 0 5 0 0
.. xo3ox .. .. .. ..&#x ♦  3  3 |   3   6   3 |  0   1   3   3   1   0 |  *   *  * 280   *  *   *   * |  0   0  1   4   0  0   0   0 |  0  0  4   6   0  0  0  0 | 0 0  6  4  0 0 0 | 0 4 1 0
.. .. ox3oo .. .. ..&#x ♦  1  3 |   0   3   3 |  0   0   0   3   0   1 |  *   *  *   * 560  *   *   * |  0   0  0   2   3  0   0   0 |  0  0  1   6   3  0  0  0 | 0 0  3  6  1 0 0 | 0 3 2 0
.o3.o3.x .. .. .. ..    ♦  0  4 |   0   0   6 |  0   0   0   0   4   0 |  *   *  *   *   * 70   *   * ♦  0   0  1   0   0  4   0   0 |  0  0  4   0   0  6  0  0 | 0 0  6  0  0 4 0 | 0 4 0 1
.. .o3.x3.o .. .. ..    ♦  0  6 |   0   0  12 |  0   0   0   0   4   4 |  *   *  *   *   *  * 280   * |  0   0  0   1   0  1   3   0 |  0  0  1   3   0  3  3  0 | 0 0  3  3  0 3 1 | 0 3 1 1
.. .. .x3.o3.o .. ..    ♦  0  4 |   0   0   6 |  0   0   0   0   0   4 |  *   *  *   *   *  *   * 420 |  0   0  0   0   1  0   2   2 |  0  0  0   2   2  1  4  1 | 0 0  1  4  1 2 2 | 0 2 2 1
------------------------+-------+-------------+------------------------+------------------------------+------------------------------+---------------------------+------------------+--------
o.3x.3o.3o. .. .. ..    ♦ 10  0 |  30   0   0 | 10  20   0   0   0   0 |  5   5  0   0   0  0   0   0 | 56   *  *   *   *  *   *   * |  3  0  1   0   0  0  0  0 | 3 0  3  0  0 0 0 | 1 3 0 0
.. x.3o.3o.3o. .. ..    ♦  5  0 |  10   0   0 |  0  10   0   0   0   0 |  0   5  0   0   0  0   0   0 |  * 168  *   *   *  *   *   * |  1  2  0   1   0  0  0  0 | 2 1  1  2  0 0 0 | 1 2 1 0
oo3xo3ox .. .. .. ..&#x ♦  6  4 |  12  12   6 |  4   4  12   6   4   0 |  1   0  4   4   0  1   0   0 |  *   * 70   *   *  *   *   * ♦  0  0  4   0   0  0  0  0 | 0 0  6  0  0 0 0 | 0 4 0 0
.. xo3ox3oo .. .. ..&#x ♦  4  6 |   6  12  12 |  0   4   6  12   4   4 |  0   1  0   4   4  0   1   0 |  *   *  * 280   *  *   *   * |  0  0  1   3   0  0  0  0 | 0 0  3  3  0 0 0 | 0 3 1 0
.. .. ox3oo3oo .. ..&#x ♦  1  4 |   0   4   6 |  0   0   0   6   0   4 |  0   0  0   0   4  0   0   1 |  *   *  *   * 420  *   *   * |  0  0  0   2   2  0  0  0 | 0 0  1  4  1 0 0 | 0 2 2 0
.o3.o3.x3.o .. .. ..    ♦  0 10 |   0   0  30 |  0   0   0   0  20  10 |  0   0  0   0   0  5   5   0 |  *   *  *   *   * 56   *   * ♦  0  0  1   0   0  3  0  0 | 0 0  3  0  0 3 0 | 0 3 0 1
.. .o3.x3.o3.o .. ..    ♦  0 10 |   0   0  30 |  0   0   0   0  10  20 |  0   0  0   0   0  0   5   5 |  *   *  *   *   *  * 168   * |  0  0  0   1   0  1  2  0 | 0 0  1  2  0 2 1 | 0 2 1 1
.. .. .x3.o3.o3.o ..    ♦  0  5 |   0   0  10 |  0   0   0   0   0  10 |  0   0  0   0   0  0   0   5 |  *   *  *   *   *  *   * 168 |  0  0  0   0   1  0  2  1 | 0 0  0  2  1 1 2 | 0 1 2 1
------------------------+-------+-------------+------------------------+------------------------------+------------------------------+---------------------------+------------------+--------
o.3x.3o.3o.3o. .. ..    ♦ 15  0 |  60   0   0 | 20  60   0   0   0   0 | 15  30  0   0   0  0   0   0 |  6   6  0   0   0  0   0   0 | 28  *  *   *   *  *  *  * | 2 0  1  0  0 0 0 | 1 2 0 0
.. x.3o.3o.3o.3o. ..    ♦  6  0 |  15   0   0 |  0  20   0   0   0   0 |  0  15  0   0   0  0   0   0 |  0   6  0   0   0  0   0   0 |  * 56  *   *   *  *  *  * | 1 1  0  1  0 0 0 | 1 1 1 0
oo3xo3ox3oo .. .. ..&#x ♦ 10 10 |  30  30  30 | 10  20  30  30  20  10 |  5   5 10  20  10  5   5   0 |  1   0  5   5   0  1   0   0 |  *  * 56   *   *  *  *  * | 0 0  3  0  0 0 0 | 0 3 0 0
.. xo3ox3oo3oo .. ..&#x ♦  5 10 |  10  20  30 |  0  10  10  30  10  20 |  0   5  0  10  20  0   5   5 |  0   1  0   5   5  0   1   0 |  *  *  * 168   *  *  *  * | 0 0  1  2  0 0 0 | 0 2 1 0
.. .. ox3oo3oo3oo ..&#x ♦  1  5 |   0   5  10 |  0   0   0  10   0  10 |  0   0  0   0  10  0   0   5 |  0   0  0   0   5  0   0   1 |  *  *  *   * 168  *  *  * | 0 0  0  2  1 0 0 | 0 1 2 0
.o3.o3.x3.o3.o .. ..    ♦  0 20 |   0   0  90 |  0   0   0   0  60  60 |  0   0  0   0   0 15  30  15 |  0   0  0   0   0  6   6   0 |  *  *  *   *   * 28  *  * | 0 0  1  0  0 2 0 | 0 2 0 1
.. .o3.x3.o3.o3.o ..    ♦  0 15 |   0   0  60 |  0   0   0   0  20  60 |  0   0  0   0   0  0  15  30 |  0   0  0   0   0  0   6   6 |  *  *  *   *   *  * 56  * | 0 0  0  1  0 1 1 | 0 1 1 1
.. .. .x3.o3.o3.o3.o    ♦  0  6 |   0   0  15 |  0   0   0   0   0  20 |  0   0  0   0   0  0   0  15 |  0   0  0   0   0  0   0   6 |  *  *  *   *   *  *  * 28 | 0 0  0  0  1 0 2 | 0 0 2 1
------------------------+-------+-------------+------------------------+------------------------------+------------------------------+---------------------------+------------------+--------
o.3x.3o.3o.3o.3o. ..    ♦ 21  0 | 105   0   0 | 35 140   0   0   0   0 | 35 105  0   0   0  0   0   0 | 21  42  0   0   0  0   0   0 |  7  7  0   0   0  0  0  0 | 8 *  *  *  * * * | 1 1 0 0
.. x.3o.3o.3o.3o.3o.    ♦  7  0 |  21   0   0 |  0  35   0   0   0   0 |  0  35  0   0   0  0   0   0 |  0  21  0   0   0  0   0   0 |  0  7  0   0   0  0  0  0 | * 8  *  *  * * * | 1 0 1 0
oo3xo3ox3oo3oo .. ..&#x ♦ 15 20 |  60  60  90 | 20  60  60  90  60  60 | 15  30 20  60  60 15  30  15 |  6   6 15  30  15  6   6   0 |  1  0  6   6   0  1  0  0 | * * 28  *  * * * | 0 2 0 0
.. xo3ox3oo3oo3oo ..&#x ♦  6 15 |  15  30  60 |  0  20  15  60  20  60 |  0  15  0  20  60  0  15  30 |  0   6  0  15  30  0   6   6 |  0  1  0   6   6  0  1  0 | * *  * 56  * * * | 0 1 1 0
.. .. ox3oo3oo3oo3oo&#x ♦  1  6 |   0   6  15 |  0   0   0  15   0  20 |  0   0  0   0  20  0   0  15 |  0   0  0   0  15  0   0   6 |  0  0  0   0   6  0  0  1 | * *  *  * 28 * * | 0 0 2 0
.o3.o3.x3.o3.o3.o ..    ♦  0 35 |   0   0 210 |  0   0   0   0 140 210 |  0   0  0   0   0 35 105 105 |  0   0  0   0   0 21  42  21 |  0  0  0   0   0  7  7  0 | * *  *  *  * 8 * | 0 1 0 1
.. .o3.x3.o3.o3.o3.o    ♦  0 21 |   0   0 105 |  0   0   0   0  35 140 |  0   0  0   0   0  0  35 105 |  0   0  0   0   0  0  21  42 |  0  0  0   0   0  0  7  7 | * *  *  *  * * 8 | 0 0 1 1
------------------------+-------+-------------+------------------------+------------------------------+------------------------------+---------------------------+------------------+--------
o.3x.3o.3o.3o.3o.3o.    ♦ 28  0 | 168   0   0 | 56 280   0   0   0   0 | 70 280  0   0   0  0   0   0 | 56 168  0   0   0  0   0   0 | 28 56  0   0   0  0  0  0 | 8 8  0  0  0 0 0 | 1 * * *
oo3xo3ox3oo3oo3oo ..&#x ♦ 21 35 | 105 105 210 | 35 140 105 210 140 210 | 35 105 35 140 210 35 105 105 | 21  42 35 105 105 21  42  21 |  7  7 21  42  21  7  7  0 | 1 0  7  7  0 1 0 | * 8 * *
.. xo3ox3oo3oo3oo3oo&#x ♦  7 21 |  21  42 105 |  0  35  21 105  35 140 |  0  35  0  35 140  0  35 105 |  0  21  0  35 105  0  21  42 |  0  7  0  21  42  0  7  7 | 0 1  0  7  7 0 1 | * * 8 *
.o3.o3.x3.o3.o3.o3.o    ♦  0 56 |   0   0 420 |  0   0   0   0 280 560 |  0   0  0   0   0 70 280 420 |  0   0  0   0   0 56 168 168 |  0  0  0   0   0 28 56 28 | 0 0  0  0  0 8 8 | * * * 1

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