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)

... 

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

... 

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

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