Acronym	bersa (old: dars)
Name	birectified hepteract, Gosset polytope 04,1,1
Circumradius	sqrt(5/2) = 1.581139
Inradius wrt. ril	5/sqrt(14) = 1.336306
Inradius wrt. brox	1/sqrt(2) = 0.707107
Lace city in approx. ASCII-art	©   n r n - o3o3o3x3o4o (brox) r Q r - o3o3o3o3x4o (rax) n r n - o3o3o3x3o4o (brox) where: n - o3o3x3o4o (nit) r - o3o3o3x4o (rin) Q - o3o3o3o4q (q-pent)
Coordinates	(1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0, 0)   & all permutations, all changes of sign
Volume	4919 sqrt(2)/630 = 11.042090
Dihedral angles	at hix between ril and ril:   arccos(-5/7) = 135.584691° at rix between brox and ril:   arccos[-1/sqrt(7)] = 112.207654° at nit between brox and brox:   90°
Face vector	672, 6720, 13440, 11760, 5656, 1428, 142
Confer	general polytopal classes: Wythoffian polyexa   Coxeter-Elte-Gosset polytopes   analogs: birectified hypercube brCn
External links

Incidence matrix according to Dynkin symbol

o3o3o3o3x3o4o

. . . . . . . | 672 ♦   20 |   40   20 |   40   40   5 |   20   40  10 |   4  20 10 |   4  5
--------------+-----+------+-----------+---------------+---------------+------------+-------
. . . . x . . |   2 | 6720 |    4    2 |    6    8   1 |    4   12   4 |   1   8  6 |   2  4
--------------+-----+------+-----------+---------------+---------------+------------+-------
. . . o3x . . |   3 |    3 | 8960    * |    3    2   0 |    3    6   1 |   1   6  3 |   2  3
. . . . x3o . |   3 |    3 |    * 4480 |    0    4   1 |    0    6   4 |   0   4  6 |   1  4
--------------+-----+------+-----------+---------------+---------------+------------+-------
. . o3o3x . . ♦   4 |    6 |    4    0 | 6720    *   * |    2    2   0 |   1   4  1 |   2  2
. . . o3x3o . ♦   6 |   12 |    4    4 |    * 4480   * |    0    3   1 |   0   3  3 |   1  3
. . . . x3o4o ♦   6 |   12 |    0    8 |    *    * 560 ♦    0    0   4 |   0   0  6 |   0  4
--------------+-----+------+-----------+---------------+---------------+------------+-------
. o3o3o3x . . ♦   5 |   10 |   10    0 |    5    0   0 | 2688    *   * |   1   2  0 |   2  1
. . o3o3x3o . ♦  10 |   30 |   20   10 |    5    5   0 |    * 2688   * |   0   2  1 |   1  2
. . . o3x3o4o ♦  24 |   96 |   32   64 |    0   16   8 |    *    * 280 |   0   0  3 |   0  3
--------------+-----+------+-----------+---------------+---------------+------------+-------
o3o3o3o3x . . ♦   6 |   15 |   20    0 |   15    0   0 |    6    0   0 | 448   *  * |   2  0
. o3o3o3x3o . ♦  15 |   60 |   60   20 |   30   15   0 |    6    6   0 |   * 896  * |   1  1
. . o3o3x3o4o ♦  80 |  480 |  320  320 |   80  160  40 |    0   32  10 |   *   * 84 |   0  2
--------------+-----+------+-----------+---------------+---------------+------------+-------
o3o3o3o3x3o . ♦  21 |  105 |  140   35 |  105   35   0 |   42   21   0 |   7   7  0 | 128  *
. o3o3o3x3o4o ♦ 240 | 1920 | 1920 1280 |  960  960 160 |  192  384  60 |   0  64 12 |   * 14

o3o3o3o3x3o4/3o

. . . . . .   . | 672 ♦   20 |   40   20 |   40   40   5 |   20   40  10 |   4  20 10 |   4  5
----------------+-----+------+-----------+---------------+---------------+------------+-------
. . . . x .   . |   2 | 6720 |    4    2 |    6    8   1 |    4   12   4 |   1   8  6 |   2  4
----------------+-----+------+-----------+---------------+---------------+------------+-------
. . . o3x .   . |   3 |    3 | 8960    * |    3    2   0 |    3    6   1 |   1   6  3 |   2  3
. . . . x3o   . |   3 |    3 |    * 4480 |    0    4   1 |    0    6   4 |   0   4  6 |   1  4
----------------+-----+------+-----------+---------------+---------------+------------+-------
. . o3o3x .   . ♦   4 |    6 |    4    0 | 6720    *   * |    2    2   0 |   1   4  1 |   2  2
. . . o3x3o   . ♦   6 |   12 |    4    4 |    * 4480   * |    0    3   1 |   0   3  3 |   1  3
. . . . x3o4/3o ♦   6 |   12 |    0    8 |    *    * 560 ♦    0    0   4 |   0   0  6 |   0  4
----------------+-----+------+-----------+---------------+---------------+------------+-------
. o3o3o3x .   . ♦   5 |   10 |   10    0 |    5    0   0 | 2688    *   * |   1   2  0 |   2  1
. . o3o3x3o   . ♦  10 |   30 |   20   10 |    5    5   0 |    * 2688   * |   0   2  1 |   1  2
. . . o3x3o4/3o ♦  24 |   96 |   32   64 |    0   16   8 |    *    * 280 |   0   0  3 |   0  3
----------------+-----+------+-----------+---------------+---------------+------------+-------
o3o3o3o3x .   . ♦   6 |   15 |   20    0 |   15    0   0 |    6    0   0 | 448   *  * |   2  0
. o3o3o3x3o   . ♦  15 |   60 |   60   20 |   30   15   0 |    6    6   0 |   * 896  * |   1  1
. . o3o3x3o4/3o ♦  80 |  480 |  320  320 |   80  160  40 |    0   32  10 |   *   * 84 |   0  2
----------------+-----+------+-----------+---------------+---------------+------------+-------
o3o3o3o3x3o   . ♦  21 |  105 |  140   35 |  105   35   0 |   42   21   0 |   7   7  0 | 128  *
. o3o3o3x3o4/3o ♦ 240 | 1920 | 1920 1280 |  960  960 160 |  192  384  60 |   0  64 12 |   * 14

o3x3o *b3o3o3o3o

. . .    . . . . | 672 ♦   20 |   10   10   40 |   5   20   20   40 |  10   20   20   20 | 10  10  10   4 |  5  2  2
-----------------+-----+------+----------------+--------------------+--------------------+----------------+---------
. x .    . . . . |   2 | 6720 |    1    1    4 |   1    4    4    6 |   4    6    6    4 |  6   4   4   1 |  4  1  1
-----------------+-----+------+----------------+--------------------+--------------------+----------------+---------
o3x .    . . . . |   3 |    3 | 2240    *    * |   1    4    0    0 |   4    4    0    0 |  6   4   0   0 |  4  1  0
. x3o    . . . . |   3 |    3 |    * 2240    * |   1    0    4    0 |   4    0    4    0 |  6   0   4   0 |  4  0  1
. x . *b3o . . . |   3 |    3 |    *    * 8960 |   0    1    1    3 |   1    3    3    3 |  3   3   3   1 |  3  1  1
-----------------+-----+------+----------------+--------------------+--------------------+----------------+---------
o3x3o    . . . . |   6 |   12 |    4    4    0 | 560    *    *    * ♦   4    0    0    0 |  6   0   0   0 |  4  0  0
o3x . *b3o . . . ♦   6 |   12 |    4    0    4 |   * 2240    *    * |   1    3    0    0 |  3   3   0   0 |  3  1  0
. x3o *b3o . . . ♦   6 |   12 |    0    4    4 |   *    * 2240    * |   1    0    3    0 |  3   0   3   0 |  3  0  1
. x . *b3o3o . . ♦   4 |    6 |    0    0    4 |   *    *    * 6720 |   0    1    1    2 |  1   2   2   1 |  2  1  1
-----------------+-----+------+----------------+--------------------+--------------------+----------------+---------
o3x3o *b3o . . . ♦  24 |   96 |   32   32   32 |   8    8    8    0 | 280    *    *    * |  3   0   0   0 |  3  0  0
o3x . *b3o3o . . ♦  10 |   30 |   10    0   20 |   0    5    0    5 |   * 1344    *    * |  1   2   0   0 |  2  1  0
. x3o *b3o3o . . ♦  10 |   30 |    0   10   20 |   0    0    5    5 |   *    * 1344    * |  1   0   2   0 |  2  0  1
. x . *b3o3o3o . ♦   5 |   10 |    0    0   10 |   0    0    0    5 |   *    *    * 2688 |  0   1   1   1 |  1  1  1
-----------------+-----+------+----------------+--------------------+--------------------+----------------+---------
o3x3o *b3o3o . . ♦  80 |  480 |  160  160  320 |  40   80   80   80 |  10   16   16    0 | 84   *   *   * |  2  0  0
o3x . *b3o3o3o . ♦  15 |   60 |   20    0   60 |   0   15    0   30 |   0    6    0    6 |  * 448   *   * |  1  1  0
. x3o *b3o3o3o . ♦  15 |   60 |    0   20   60 |   0    0   15   30 |   0    0    6    6 |  *   * 448   * |  1  0  1
. x . *b3o3o3o3o ♦   6 |   15 |    0    0   20 |   0    0    0   15 |   0    0    0    6 |  *   *   * 448 |  0  1  1
-----------------+-----+------+----------------+--------------------+--------------------+----------------+---------
o3x3o *b3o3o3o . ♦ 240 | 1920 |  640  640 1920 | 160  480  480  960 |  60  192  192  192 | 12  32  32   0 | 14  *  *
o3x . *b3o3o3o3o ♦  21 |  105 |   35    0  140 |   0   35    0  105 |   0   21    0   42 |  0   7   0   7 |  * 64  *
. x3o *b3o3o3o3o ♦  21 |  105 |    0   35  140 |   0    0   35  105 |   0    0   21   42 |  0   0   7   7 |  *  * 64

ooo3ooo3ooo3xox3oxo4ooo&#xt   → both heights = 1/sqrt(2) = 0.707107
(brox || pseudo rax || brox)

o..3o..3o..3o..3o..4o..     | 240   *   * ♦   16   4   0   0    0 |   24   16   16   4    0    0   0    0    0 |  16  24   4   24   16   1   0    0    0   0   0   0 |   4  16  6  16  24   4   0   0   0   0   0  0 |  4  4   4  16  6  0   0   0  0  0 | 1  4  4  0 0
.o.3.o.3.o.3.o.3.o.4.o.     |   * 192   * ♦    0   5  10   5    0 |    0    0   10  10   20   10  10    0    0 |   0   0   0   10   20   5  20   10   20   0   0   0 |   0   0  0   5  20  10  10   5  20   0   0  0 |  0  0   1  10 10  2   1  10  0  0 | 0  2  5  2 0
..o3..o3..o3..o3..o4..o     |   *   * 240 ♦    0   0   0   4   16 |    0    0    0   0    0   16   4   24   16 |   0   0   0    0    0   1   0   24   16  16  24   4 |   0   0  0   0   0   4   0  16  24   4  16  6 |  0  0   0   0  6  0   4  16  4  4 | 0  0  4  4 1
----------------------------+-------------+-----------------------+--------------------------------------------+-----------------------------------------------------+-----------------------------------------------+-----------------------------------+-------------
... ... ... x.. ... ...     |   2   0   0 | 1920   *   *   *    * |    3    2    1   0    0    0   0    0    0 |   3   6   1    3    2   0   0    0    0   0   0   0 |   1   6  3   3   6   1   0   0   0   0   0  0 |  2  3   1   6  3  0   0   0  0  0 | 1  2  3  0 0
oo.3oo.3oo.3oo.3oo.4oo.&#x  |   1   1   0 |    * 960   *   *    * |    0    0    4   2    0    0   0    0    0 |   0   0   0    6    8   1   0    0    0   0   0   0 |   0   0  0   4  12   4   0   0   0   0   0  0 |  0  0   1   8  6  0   0   0  0  0 | 0  2  4  0 0
... ... ... ... .x. ...     |   0   2   0 |    *   * 960   *    * |    0    0    0   1    4    0   1    0    0 |   0   0   0    0    4   1   6    0    4   0   0   0 |   0   0  0   0   6   4   4   0   6   0   0  0 |  0  0   0   4  6  1   0   4  0  0 | 0  1  4  1 0
.oo3.oo3.oo3.oo3.oo3.oo&#x  |   0   1   1 |    *   *   * 960    * |    0    0    0   0    0    4   2    0    0 |   0   0   0    0    0   1   0    6    8   0   0   0 |   0   0  0   0   0   4   0   4  12   0   0  0 |  0  0   0   0  6  0   1   8  0  0 | 0  0  4  2 0
... ... ... ..x ... ...     |   0   0   2 |    *   *   *   * 1920 |    0    0    0   0    0    1   0    3    2 |   0   0   0    0    0   0   0    3    2   3   6   1 |   0   0  0   0   0   1   0   3   6   1   6  3 |  0  0   0   0  3  0   1   6  2  3 | 0  0  3  2 1
----------------------------+-------------+-----------------------+--------------------------------------------+-----------------------------------------------------+-----------------------------------------------+-----------------------------------+-------------
... ... o..3x.. ... ...     |   3   0   0 |    3   0   0   0    0 | 1920    *    *   *    *    *   *    *    * |   2   2   0    1    0   0   0    0    0   0   0   0 |   1   4  1   2   2   0   0   0   0   0   0  0 |  2  2   1   4  1  0   0   0  0  0 | 1  2  2  0 0
... ... ... x..3o.. ...     |   3   0   0 |    3   0   0   0    0 |    * 1280    *   *    *    *   *    *    * |   0   3   1    0    1   0   0    0    0   0   0   0 |   0   3  3   0   3   1   0   0   0   0   0  0 |  1  3   0   3  3  0   0   0  0  0 | 1  1  3  0 0
... ... ... xo. ... ...&#x  |   2   1   0 |    1   2   0   0    0 |    *    * 1920   *    *    *   *    *    * |   0   0   0    3    2   0   0    0    0   0   0   0 |   0   0  0   3   6   1   0   0   0   0   0  0 |  0  0   1   6  3  0   0   0  0  0 | 0  2  3  0 0
... ... ... ... ox. ...&#x  |   1   2   0 |    0   2   1   0    0 |    *    *    * 960    *    *   *    *    * |   0   0   0    0    4   1   0    0    0   0   0   0 |   0   0  0   0   6   4   0   0   0   0   0  0 |  0  0   0   4  6  0   0   0  0  0 | 0  1  4  0 0
... ... ... .o.3.x. ...     |   0   3   0 |    0   0   3   0    0 |    *    *    *   * 1280    *   *    *    * |   0   0   0    0    1   0   3    0    1   0   0   0 |   0   0  0   0   3   1   3   0   3   0   0  0 |  0  0   0   3  3  1   0   3  0  0 | 0  1  3  1 0
... ... ... .ox ... ...&#x  |   0   1   2 |    0   0   0   2    1 |    *    *    *   *    * 1920   *    *    * |   0   0   0    0    0   0   0    3    2   0   0   0 |   0   0  0   0   0   1   0   3   6   0   0  0 |  0  0   0   0  3  0   1   6  0  0 | 0  0  3  2 0
... ... ... ... .xo ...&#x  |   0   2   1 |    0   0   1   2    0 |    *    *    *   *    *    * 960    *    * |   0   0   0    0    0   1   0    0    4   0   0   0 |   0   0  0   0   0   4   0   0   6   0   0  0 |  0  0   0   0  6  0   0   4  0  0 | 0  0  4  1 0
... ... ..o3..x ... ...     |   0   0   3 |    0   0   0   0    3 |    *    *    *   *    *    *   * 1920    * |   0   0   0    0    0   0   0    1    0   2   2   0 |   0   0  0   0   0   0   0   2   2   1   4  1 |  0  0   0   0  1  0   1   4  2  2 | 0  0  2  2 1
... ... ... ..x3..o ...     |   0   0   3 |    0   0   0   0    3 |    *    *    *   *    *    *   *    * 1280 |   0   0   0    0    0   0   0    0    1   0   3   1 |   0   0  0   0   0   1   0   0   3   0   3  3 |  0  0   0   0  3  0   0   3  1  3 | 0  0  3  1 1
----------------------------+-------------+-----------------------+--------------------------------------------+-----------------------------------------------------+-----------------------------------------------+-----------------------------------+-------------
... o..3o..3x.. ... ...     ♦   4   0   0 |    6   0   0   0    0 |    4    0    0   0    0    0   0    0    0 | 960   *   *    *    *   *   *    *    *   *   *   * |   1   2  0   1   0   0   0   0   0   0   0  0 |  2  1   1   2  0  0   0   0  0  0 | 1  2  1  0 0
... ... o..3x..3o.. ...     ♦   6   0   0 |   12   0   0   0    0 |    4    4    0   0    0    0   0    0    0 |   * 960   *    *    *   *   *    *    *   *   *   * |   0   2  1   0   1   0   0   0   0   0   0  0 |  1  2   0   2  1  0   0   0  0  0 | 1  1  2  0 0
... ... ... x..3o..4o..     ♦   6   0   0 |   12   0   0   0    0 |    0    8    0   0    0    0   0    0    0 |   *   * 160    *    *   *   *    *    *   *   *   * ♦   0   0  3   0   0   1   0   0   0   0   0  0 |  0  3   0   0  3  0   0   0  0  0 | 1  0  3  0 0
... ... oo.3xo. ... ...&#x  ♦   3   1   0 |    3   3   0   0    0 |    1    0    3   0    0    0   0    0    0 |   *   *   * 1920    *   *   *    *    *   *   *   * |   0   0  0   2   2   0   0   0   0   0   0  0 |  0  0   1   4  1  0   0   0  0  0 | 0  2  2  0 0
... ... ... xo.3ox. ...&#x  ♦   3   3   0 |    3   6   3   0    0 |    0    1    3   3    1    0   0    0    0 |   *   *   *    * 1280   *   *    *    *   *   *   * |   0   0  0   0   3   1   0   0   0   0   0  0 |  0  0   0   3  3  0   0   0  0  0 | 0  1  3  0 0
... ... ... ... oxo4ooo&#xt ♦   1   4   1 |    0   4   4   4    0 |    0    0    0   4    0    0   4    0    0 |   *   *   *    *    * 240   *    *    *   *   *   * ♦   0   0  0   0   0   4   0   0   0   0   0  0 |  0  0   0   0  6  0   0   0  0  0 | 0  0  4  0 0
... ... .o.3.o.3.x. ...     ♦   0   4   0 |    0   0   6   0    0 |    0    0    0   0    4    0   0    0    0 |   *   *   *    *    *   * 960    *    *   *   *   * |   0   0  0   0   1   0   2   0   1   0   0  0 |  0  0   0   2  1  1   0   2  0  0 | 0  1  2  1 0
... ... .oo3.ox ... ...&#x  ♦   0   1   3 |    0   0   0   3    3 |    0    0    0   0    0    3   0    1    0 |   *   *   *    *    *   *   * 1920    *   *   *   * |   0   0  0   0   0   0   0   2   2   0   0  0 |  0  0   0   0  1  0   1   4  0  0 | 0  0  2  2 0
... ... ... .ox3.xo ...&#x  ♦   0   3   3 |    0   0   3   6    3 |    0    0    0   0    1    3   3    0    1 |   *   *   *    *    *   *   *    * 1280   *   *   * |   0   0  0   0   0   1   0   0   3   0   0  0 |  0  0   0   0  3  0   0   3  0  0 | 0  0  3  1 0
... ..o3..o3..x ... ...     ♦   0   0   4 |    0   0   0   0    6 |    0    0    0   0    0    0   0    4    0 |   *   *   *    *    *   *   *    *    * 960   *   * |   0   0  0   0   0   0   0   1   0   1   2  0 |  0  0   0   0  0  0   1   2  2  1 | 0  0  1  2 1
... ... ..o3..x3..o ...     ♦   0   0   6 |    0   0   0   0   12 |    0    0    0   0    0    0   0    4    4 |   *   *   *    *    *   *   *    *    *   * 960   * |   0   0  0   0   0   0   0   0   1   0   2  1 |  0  0   0   0  1  0   0   2  1  2 | 0  0  2  1 1
... ... ... ..x3..o4..o     ♦   0   0   6 |    0   0   0   0   12 |    0    0    0   0    0    0   0    0    8 |   *   *   *    *    *   *   *    *    *   *   * 160 ♦   0   0  0   0   0   1   0   0   0   0   0  3 |  0  0   0   0  3  0   0   0  0  3 | 0  0  3  0 1
----------------------------+-------------+-----------------------+--------------------------------------------+-----------------------------------------------------+-----------------------------------------------+-----------------------------------+-------------
o..3o..3o..3x.. ... ...     ♦   5   0   0 |   10   0   0   0    0 |   10    0    0   0    0    0   0    0    0 |   5   0   0    0    0   0   0    0    0   0   0   0 | 192   *  *   *   *   *   *   *   *   *   *  * |  2  0   1   0  0  0   0   0  0  0 | 1  2  0  0 0
... o..3o..3x..3o.. ...     ♦  10   0   0 |   30   0   0   0    0 |   20   10    0   0    0    0   0    0    0 |   5   5   0    0    0   0   0    0    0   0   0   0 |   * 384  *   *   *   *   *   *   *   *   *  * |  1  1   0   1  0  0   0   0  0  0 | 1  1  1  0 0
... ... o..3x..3o..4o..     ♦  24   0   0 |   96   0   0   0    0 |   32   64    0   0    0    0   0    0    0 |   0  16   8    0    0   0   0    0    0   0   0   0 |   *   * 60   *   *   *   *   *   *   *   *  * |  0  2   0   0  1  0   0   0  0  0 | 1  0  2  0 0
... oo.3oo.3xo. ... ...&#x  ♦   4   1   0 |    6   4   0   0    0 |    4    0    6   0    0    0   0    0    0 |   1   0   0    4    0   0   0    0    0   0   0   0 |   *   *  * 960   *   *   *   *   *   *   *  * |  0  0   1   2  0  0   0   0  0  0 | 0  2  1  0 0
... ... oo.3xo.3ox. ...&#x  ♦   6   4   0 |   12  12   6   0    0 |    4    4   12   6    4    0   0    0    0 |   0   1   0    4    4   0   1    0    0   0   0   0 |   *   *  *   * 960   *   *   *   *   *   *  * |  0  0   0   2  1  0   0   0  0  0 | 0  1  2  0 0
... ... ... xox3oxo4ooo&#xt ♦   6  12   6 |   12  24  24  24   12 |    0    8   12  24    8   12  24    0    8 |   0   0   1    0    8   6   0    0    8   0   0   1 |   *   *  *   *   * 160   *   *   *   *   *  * |  0  0   0   0  3  0   0   0  0  0 | 0  0  3  0 0
... .o.3.o.3.o.3.x. ...     ♦   0   5   0 |    0   0  10   0    0 |    0    0    0   0   10    0   0    0    0 |   0   0   0    0    0   0   5    0    0   0   0   0 |   *   *  *   *   *   * 384   *   *   *   *  * |  0  0   0   1  0  1   0   1  0  0 | 0  1  1  1 0
... .oo3.oo3.ox ... ...&#x  ♦   0   1   4 |    0   0   0   4    6 |    0    0    0   0    0    6   0    4    0 |   0   0   0    0    0   0   0    4    0   1   0   0 |   *   *  *   *   *   *   * 960   *   *   *  * |  0  0   0   0  0  0   1   2  0  0 | 0  0  1  2 0
... ... .oo3.ox3.xo ...&#x  ♦   0   4   6 |    0   0   6  12   12 |    0    0    0   0    4   12   6    4    4 |   0   0   0    0    0   0   1    4    4   0   1   0 |   *   *  *   *   *   *   *   * 960   *   *  * |  0  0   0   0  1  0   0   2  0  0 | 0  0  2  1 0
..o3..o3..o3..x ... ...     ♦   0   0   5 |    0   0   0   0   10 |    0    0    0   0    0    0   0   10    0 |   0   0   0    0    0   0   0    0    0   5   0   0 |   *   *  *   *   *   *   *   *   * 192   *  * |  0  0   0   0  0  0   1   0  2  0 | 0  0  0  2 1
... ..o3..o3..x3..o ...     ♦   0   0  10 |    0   0   0   0   30 |    0    0    0   0    0    0   0   20   10 |   0   0   0    0    0   0   0    0    0   5   5   0 |   *   *  *   *   *   *   *   *   *   * 384  * |  0  0   0   0  0  0   0   1  1  1 | 0  0  1  1 1
... ... ..o3..x3..o4..o     ♦   0   0  24 |    0   0   0   0   96 |    0    0    0   0    0    0   0   32   64 |   0   0   0    0    0   0   0    0    0   0  16   8 |   *   *  *   *   *   *   *   *   *   *   * 60 |  0  0   0   0  1  0   0   0  0  2 | 0  0  2  0 1
----------------------------+-------------+-----------------------+--------------------------------------------+-----------------------------------------------------+-----------------------------------------------+-----------------------------------+-------------
o..3o..3o..3x..3o.. ...     ♦  15   0   0 |   60   0   0   0    0 |   60   20    0   0    0    0   0    0    0 |  30  15   0    0    0   0   0    0    0   0   0   0 |   6   6  0   0   0   0   0   0   0   0   0  0 | 64  *   *   *  *  *   *   *  *  * | 1  1  0  0 0
... o..3o..3x..3o..4o..     ♦  80   0   0 |  480   0   0   0    0 |  320  320    0   0    0    0   0    0    0 |  80 160  40    0    0   0   0    0    0   0   0   0 |   0  32 10   0   0   0   0   0   0   0   0  0 |  * 12   *   *  *  *   *   *  *  * | 1  0  1  0 0
oo.3oo.3oo.3xo. ... ...&#x  ♦   5   1   0 |   10   5   0   0    0 |   10    0   10   0    0    0   0    0    0 |   5   0   0   10    0   0   0    0    0   0   0   0 |   1   0  0   5   0   0   0   0   0   0   0  0 |  *  * 192   *  *  *   *   *  *  * | 0  2  0  0 0
... oo.3oo.3xo.3ox. ...&#x  ♦  10   5   0 |   30  20  10   0    0 |   20   10   30  10   10    0   0    0    0 |   5   5   0   20   10   0   5    0    0   0   0   0 |   0   1  0   5   5   0   1   0   0   0   0  0 |  *  *   * 384  *  *   *   *  *  * | 0  1  1  0 0
... ... ooo3xox3oxo4ooo&#xt ♦  24  32  24 |   96  96  96  96   96 |   32   64   96  96   64   96  96   32   64 |   0  16   8   32   64  24  16   32   64   0  16   8 |   0   0  1   0  16   8   0   0  16   0   0  1 |  *  *   *   * 60  *   *   *  *  * | 0  0  2  0 0
.o.3.o.3.o.3.o.3.x. ...     ♦   0   6   0 |    0   0  15   0    0 |    0    0    0   0   20    0   0    0    0 |   0   0   0    0    0   0  15    0    0   0   0   0 |   0   0  0   0   0   0   6   0   0   0   0  0 |  *  *   *   *  * 64   *   *  *  * | 0  1  0  1 0
.oo3.oo3.oo3.ox ... ...&#x  ♦   0   1   5 |    0   0   0   5   10 |    0    0    0   0    0   10   0   10    0 |   0   0   0    0    0   0   0   10    0   5   0   0 |   0   0  0   0   0   0   0   5   0   1   0  0 |  *  *   *   *  *  * 192   *  *  * | 0  0  0  2 0
... .oo3.oo3.ox3.xo ...&#x  ♦   0   5  10 |    0   0  10  20   30 |    0    0    0   0   10   30  10   20   10 |   0   0   0    0    0   0   5   20   10   5   5   0 |   0   0  0   0   0   0   1   5   5   0   1  0 |  *  *   *   *  *  *   * 384  *  * | 0  0  1  1 0
..o3..o3..o3..x3..o ...     ♦   0   0  15 |    0   0   0   0   60 |    0    0    0   0    0    0   0   60   20 |   0   0   0    0    0   0   0    0    0  30  15   0 |   0   0  0   0   0   0   0   0   0   6   6  0 |  *  *   *   *  *  *   *   * 64  * | 0  0  0  1 1
... ..o3..o3..x3..o4..o     ♦   0   0  80 |    0   0   0   0  480 |    0    0    0   0    0    0   0  320  320 |   0   0   0    0    0   0   0    0    0  80 160  40 |   0   0  0   0   0   0   0   0   0   0  32 10 |  *  *   *   *  *  *   *   *  * 12 | 0  0  1  0 1
----------------------------+-------------+-----------------------+--------------------------------------------+-----------------------------------------------------+-----------------------------------------------+-----------------------------------+-------------
o..3o..3o..3x..3o..4o..     ♦ 240   0   0 | 1920   0   0   0    0 | 1920 1280    0   0    0    0   0    0    0 | 960 960 160    0    0   0   0    0    0   0   0   0 | 192 384 60   0   0   0   0   0   0   0   0  0 | 64 12   0   0  0  0   0   0  0  0 | 1  *  *  * *
oo.3oo.3oo.3xo.3ox. ...&#x  ♦  15   6   0 |   60  30  15   0    0 |   60   20   60  15   20    0   0    0    0 |  30  15   0   60   20   0  15    0    0   0   0   0 |   6   6  0  30  15   0   6   0   0   0   0  0 |  1  0   6   6  0  1   0   0  0  0 | * 64  *  * *
... ooo3ooo3xox3oxo4ooo&#xt ♦  80  80  80 |  480 320 320 320  480 |  320  320  480 320  320  480 320  320  320 |  80 160  40  320  320  80 160  320  320  80 160  40 |   0  32 10  80 160  40  32  80 160   0  32 10 |  0  1   0  32 10  0   0  32  0  1 | *  * 12  * *
.oo3.oo3.oo3.ox3.xo ...&#x  ♦   0   6  15 |    0   0  15  30   60 |    0    0    0   0   20   60  15   60   20 |   0   0   0    0    0   0  15   60   20  30  15   0 |   0   0  0   0   0   0   6  30  15   6   6  0 |  0  0   0   0  0  1   6   6  1  0 | *  *  * 64 *
..o3..o3..o3..x3..o4..o     ♦   0   0 240 |    0   0   0   0 1920 |    0    0    0   0    0    0   0 1920 1280 |   0   0   0    0    0   0   0    0    0 960 960 160 |   0   0  0   0   0   0   0   0   0 192 384 60 |  0  0   0   0  0  0   0   0 64 12 | *  *  *  * 1

qo oo3oo3oo3xo3ox4oo&#zx   → height = 0
(tegum sum of q-height brox prism and equatorial rax)

o. o.3o.3o.3o.3o.4o.     | 480   * ♦   16    4   0 |   24   16   16    4    0 |   16   24   4   1   24   16   0 |   4  16   6   4   16   24   0 |   4  4  6   4  16  0 | 1  4   4
.o .o3.o3.o3.o3.o4.o     |   * 192 ♦    0   10  10 |    0    0   20   20   20 |    0    0   0   5   20   40  20 |   0   0   0  10   10   40  10 |   0  0 10   2  20  2 | 0  5   4
-------------------------+---------+---------------+--------------------------+---------------------------------+-------------------------------+----------------------+---------
.. .. .. .. x. .. ..     |   2   0 | 3840    *   * |    3    2    1    0    0 |    3    6   1   0    3    2   0 |   1   6   3   1    3    6   0 |   2  3  3   1   6  0 | 1  3   2
oo oo3oo3oo3oo3oo4oo&#x  |   1   1 |    * 1920   * |    0    0    4    2    0 |    0    0   0   1    6    8   0 |   0   0   0   4    4   12   0 |   0  0  6   1   8  0 | 0  4   2
.. .. .. .. .. .x ..     |   0   2 |    *    * 960 |    0    0    0    2    4 |    0    0   0   1    0    8   6 |   0   0   0   4    0   12   4 |   0  0  6   0   8  1 | 0  4   2
-------------------------+---------+---------------+--------------------------+---------------------------------+-------------------------------+----------------------+---------
.. .. .. o.3x. .. ..     |   3   0 |    3    0   0 | 3840    *    *    *    * |    2    2   0   0    0    1   0 |   1   4   1   0    2    2   0 |   2  2  1   1   4  0 | 1  2   2
.. .. .. .. x.3o. ..     |   3   0 |    3    0   0 |    * 2560    *    *    * |    0    3   1   0    0    1   0 |   0   3   3   1    0    3   0 |   1  3  3   0   3  0 | 1  3   1
.. .. .. .. xo .. ..&#x  |   2   1 |    1    2   0 |    *    * 3840    *    * |    0    0   0   0    3    2   0 |   0   0   0   1    3    6   0 |   0  0  3   1   6  0 | 0  3   2
.. .. .. .. .. ox ..&#x  |   1   2 |    0    2   1 |    *    *    * 1920    * |    0    0   0   1    0    4   0 |   0   0   0   4    0    6   0 |   0  0  6   0   4  0 | 0  4   1
.. .. .. .. .o3.x ..     |   0   3 |    0    0   3 |    *    *    *    * 1280 |    0    0   0   0    0    2   3 |   0   0   0   1    0    6   3 |   0  0  3   0   6  1 | 0  3   2
-------------------------+---------+---------------+--------------------------+---------------------------------+-------------------------------+----------------------+---------
.. .. o.3o.3x. .. ..     ♦   4   0 |    6    0   0 |    4    0    0    0    0 | 1920    *   *   *    *    *   * |   1   2   0   0    1    0   0 |   2  1  0   1   2  0 | 1  1   2
.. .. .. o.3x.3o. ..     ♦   6   0 |   12    0   0 |    4    4    0    0    0 |    * 1920   *   *    *    *   * |   0   2   1   0    0    1   0 |   1  2  1   0   2  0 | 1  2   1
.. .. .. .. x.3o.4o.     ♦   6   0 |   12    0   0 |    0    8    0    0    0 |    *    * 320   *    *    *   * ♦   0   0   3   1    0    0   0 |   0  3  3   0   0  0 | 1  3   0
qo .. .. .. .. ox4oo&#zx ♦   2   4 |    0    8   4 |    0    0    0    8    0 |    *    *   * 240    *    *   * ♦   0   0   0   4    0    0   0 |   0  0  6   0   0  0 | 0  4   0
.. .. .. oo3xo .. ..&#x  ♦   3   1 |    3    3   0 |    1    0    3    0    0 |    *    *   *   * 3840    *   * |   0   0   0   0    2    2   0 |   0  0  1   1   4  0 | 0  2   2
.. .. .. .. xo3ox ..&#x  ♦   3   3 |    3    6   3 |    0    1    3    3    1 |    *    *   *   *    * 2560   * |   0   0   0   1    0    3   0 |   0  0  3   0   3  0 | 0  3   1
.. .. .. .o3.o3.x ..     ♦   0   4 |    0    0   6 |    0    0    0    0    4 |    *    *   *   *    *    * 960 |   0   0   0   0    0    2   2 |   0  0  1   0   4  1 | 0  2   2
-------------------------+---------+---------------+--------------------------+---------------------------------+-------------------------------+----------------------+---------
.. o.3o.3o.3x. .. ..     ♦   5   0 |   10    0   0 |   10    0    0    0    0 |    5    0   0   0    0    0   0 | 384   *   *   *    *    *   * |   2  0  0   1   0  0 | 1  0   2
.. .. o.3o.3x.3o. ..     ♦  10   0 |   30    0   0 |   20   10    0    0    0 |    5    5   0   0    0    0   0 |   * 768   *   *    *    *   * |   1  1  0   0   1  0 | 1  1   1
.. .. .. o.3x.3o.4o.     ♦  24   0 |   96    0   0 |   32   64    0    0    0 |    0   16   8   0    0    0   0 |   *   * 120   *    *    *   * |   0  2  1   0   0  0 | 1  2   0
qo .. .. .. xo3ox4oo&#zx ♦  12  12 |   24   48  24 |    0   16   24   48    8 |    0    0   2   6    0   16   0 |   *   *   * 160    *    *   * |   0  0  3   0   0  0 | 0  3   0
.. .. oo3oo3xo .. ..&#x  ♦   4   1 |    6    4   0 |    4    0    6    0    0 |    1    0   0   0    4    0   0 |   *   *   *   * 1920    *   * |   0  0  0   1   2  0 | 0  1   2
.. .. .. oo3xo3ox ..&#x  ♦   6   4 |   12   12   6 |    4    4   12    6    4 |    0    1   0   0    4    4   1 |   *   *   *   *    * 1920   * |   0  0  1   0   2  0 | 0  2   1
.. .. .o3.o3.o3.x ..     ♦   0   5 |    0    0  10 |    0    0    0    0   10 |    0    0   0   0    0    0   5 |   *   *   *   *    *    * 384 |   0  0  0   0   2  1 | 0  1   2
-------------------------+---------+---------------+--------------------------+---------------------------------+-------------------------------+----------------------+---------
.. o.3o.3o.3x.3o. ..     ♦  15   0 |   60    0   0 |   60   20    0    0    0 |   30   15   0   0    0    0   0 |   6   6   0   0    0    0   0 | 128  *  *   *   *  * | 1  0   1
.. .. o.3o.3x.3o.4o.     ♦  80   0 |  480    0   0 |  320  320    0    0    0 |   80  160  40   0    0    0   0 |   0  32  10   0    0    0   0 |   * 24  *   *   *  * | 1  1   0
qo .. .. oo3xo3ox4oo&#zx ♦  48  32 |  192  192  96 |   64  128  192  192   64 |    0   32  16  24   64  128  16 |   0   0   2   8    0   32   0 |   *  * 60   *   *  * | 0  2   0
.. oo3oo3oo3xo .. ..&#x  ♦   5   1 |   10    5   0 |   10    0   10    0    0 |    5    0   0   0   10    0   0 |   1   0   0   0    5    0   0 |   *  *  * 384   *  * | 0  0   2
.. .. oo3oo3xo3ox ..&#x  ♦  10   5 |   30   20  10 |   20   10   30   10   10 |    5    5   0   0   20   10   5 |   0   1   0   0    5    5   1 |   *  *  *   * 768  * | 0  1   1
.. .o3.o3.o3.o3.x ..     ♦   0   6 |    0    0  15 |    0    0    0    0   20 |    0    0   0   0    0    0  15 |   0   0   0   0    0    0   6 |   *  *  *   *   * 64 | 0  0   2
-------------------------+---------+---------------+--------------------------+---------------------------------+-------------------------------+----------------------+---------
.. o.3o.3o.3x.3o.4o.     ♦ 240   0 | 1920    0   0 | 1920 1280    0    0    0 |  960  960 160   0    0    0   0 | 192 384  60   0    0    0   0 |  64 12  0   0   0  0 | 2  *   *
qo .. oo3oo3xo3ox4oo&#zx ♦ 160  80 |  960  640 320 |  640  640  960  640  320 |  160  320  80  80  640  640 160 |   0  64  20  40  160  320  32 |   0  2 10   0  64  0 | * 12   *
.. oo3oo3oo3xo3ox ..&#x  ♦  15   6 |   60   30  15 |   60   20   60   15   20 |   30   15   0   0   60   20  15 |   6   6   0   0   30   15   6 |   1  0  0   6   6  1 | *  * 128

oxoooo3xoxooo3oxoxoo3ooxoxo3oooxox3ooooxo&#xt   → all heights = sqrt(2/7) = 0.534522
(ril || pseudo sril || pseudo sabril || pseudo sabril || pseudo inv. sril || inv. ril)

...