Acronym	bark
Name	birectified diacosipentacontahexazetton, equatorial cross-section of rek-first brav
Circumradius	sqrt(3/2) = 1.224745
Inradius wrt. broc	3/4 = 0.75
Inradius wrt. rez	1/sqrt(2) = 0.707107
Lace city in approx. ASCII-art	©   g r g -- o3x3o3o3o3o4o (rez) r b r -- o3o3x3o3o3o4o (barz) g r g -- o3x3o3o3o3o4o (rez) where: g = x3o3o3o3o4o (gee) r = o3x3o3o3o4o (rag) b = o3o3x3o3o4o (brag)
Coordinates	(1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0, 0, 0, 0, 0)   & all permutations, all changes of sign
Volume	4541/2520 = 1.801984
Surface	(4764+968 sqrt(2))/315 = 19.469710
Dihedral angles (at margins)	at bril between broc and broc:   arccos(-5/7) = 135.584691° at ril between broc and rez:   arccos[-1/sqrt(7)] = 112.207654° at gee between rez and rez:   90°
Face vector	448, 6720, 22400, 36960, 34048, 16128, 3184, 272
Confer	related segmentozetta: rezabarz   general polytopal classes: Wythoffian polyzetta   segmentozetta   fundamental lace prisms   analogs: birectified orthoplex brOn
External links

Incidence matrix according to Dynkin symbol

o3o3x3o3o3o3o4o

. . . . . . . . | 448 ♦   30 |   30   120 |   10  120   240 |   40   240   240 |   80  240   96 |   80   96   3 |  32  3
----------------+-----+------+------------+-----------------+------------------+----------------+---------------+-------
. . x . . . . . |   2 | 6720 |    3     8 |    1   16    24 |    8    48    32 |   24   64   16 |   32   32   1 |  16  2
----------------+-----+------+------------+-----------------+------------------+----------------+---------------+-------
. o3x . . . . . |   3 |    3 | 4480     * |    1    8     0 |    8    24     0 |   24   32    0 |   32   16   0 |  16  1
. . x3o . . . . |   3 |    3 |    * 17920 |    0    2     6 |    1    12    12 |    6   24    8 |   12   16   1 |   8  2
----------------+-----+------+------------+-----------------+------------------+----------------+---------------+-------
o3o3x . . . . . ♦   4 |    6 |    4     0 | 1120    *     * ♦    8     0     0 |   24    0    0 |   32    0   0 |  16  0
. o3x3o . . . . ♦   6 |   12 |    4     4 |    * 8960     * |    1     6     0 |    6   12    0 |   12    8   0 |   8  1
. . x3o3o . . . ♦   4 |    6 |    0     4 |    *    * 26880 |    0     2     4 |    1    8    4 |    4    8   1 |   4  2
----------------+-----+------+------------+-----------------+------------------+----------------+---------------+-------
o3o3x3o . . . . ♦  10 |   30 |   20    10 |    5    5     0 | 1792     *     * ♦    6    0    0 |   12    0   0 |   8  0
. o3x3o3o . . . ♦  10 |   30 |   10    20 |    0    5     5 |    * 10752     * |    1    4    0 |    4    4   0 |   4  1
. . x3o3o3o . . ♦   5 |   10 |    0    10 |    0    0     5 |    *     * 21504 |    0    2    2 |    1    4   1 |   2  2
----------------+-----+------+------------+-----------------+------------------+----------------+---------------+-------
o3o3x3o3o . . . ♦  20 |   90 |   60    60 |   15   30    15 |    6     6     0 | 1792    *    * |    4    0   0 |   4  0
. o3x3o3o3o . . ♦  15 |   60 |   20    60 |    0   15    30 |    0     6     6 |    * 7168    * |    1    2   0 |   2  1
. . x3o3o3o3o . ♦   6 |   15 |    0    20 |    0    0    15 |    0     0     6 |    *    * 7168 |    0    2   1 |   1  2
----------------+-----+------+------------+-----------------+------------------+----------------+---------------+-------
o3o3x3o3o3o . . ♦  35 |  210 |  140   210 |   35  105   105 |   21    42    21 |    7    7    0 | 1024    *   * |   2  0
. o3x3o3o3o3o . ♦  21 |  105 |   35   140 |    0   35   105 |    0    21    42 |    0    7    7 |    * 2048   * |   1  1
. . x3o3o3o3o4o ♦  12 |   60 |    0   160 |    0    0   240 |    0     0   192 |    0    0   64 |    *    * 112 |   0  2
----------------+-----+------+------------+-----------------+------------------+----------------+---------------+-------
o3o3x3o3o3o3o . ♦  56 |  420 |  280   560 |   70  280   420 |   56   168   168 |   28   56   28 |    8    8   0 | 256  *
. o3x3o3o3o3o4o ♦  84 |  840 |  280  2240 |    0  560  3360 |    0   672  2688 |    0  448  896 |    0  128  14 |   * 16

o3o3x3o3o3o3o4/3o

. . . . . . .   . | 448 ♦   30 |   30   120 |   10  120   240 |   40   240   240 |   80  240   96 |   80   96   3 |  32  3
------------------+-----+------+------------+-----------------+------------------+----------------+---------------+-------
. . x . . . .   . |   2 | 6720 |    3     8 |    1   16    24 |    8    48    32 |   24   64   16 |   32   32   1 |  16  2
------------------+-----+------+------------+-----------------+------------------+----------------+---------------+-------
. o3x . . . .   . |   3 |    3 | 4480     * |    1    8     0 |    8    24     0 |   24   32    0 |   32   16   0 |  16  1
. . x3o . . .   . |   3 |    3 |    * 17920 |    0    2     6 |    1    12    12 |    6   24    8 |   12   16   1 |   8  2
------------------+-----+------+------------+-----------------+------------------+----------------+---------------+-------
o3o3x . . . .   . ♦   4 |    6 |    4     0 | 1120    *     * ♦    8     0     0 |   24    0    0 |   32    0   0 |  16  0
. o3x3o . . .   . ♦   6 |   12 |    4     4 |    * 8960     * |    1     6     0 |    6   12    0 |   12    8   0 |   8  1
. . x3o3o . .   . ♦   4 |    6 |    0     4 |    *    * 26880 |    0     2     4 |    1    8    4 |    4    8   1 |   4  2
------------------+-----+------+------------+-----------------+------------------+----------------+---------------+-------
o3o3x3o . . .   . ♦  10 |   30 |   20    10 |    5    5     0 | 1792     *     * ♦    6    0    0 |   12    0   0 |   8  0
. o3x3o3o . .   . ♦  10 |   30 |   10    20 |    0    5     5 |    * 10752     * |    1    4    0 |    4    4   0 |   4  1
. . x3o3o3o .   . ♦   5 |   10 |    0    10 |    0    0     5 |    *     * 21504 |    0    2    2 |    1    4   1 |   2  2
------------------+-----+------+------------+-----------------+------------------+----------------+---------------+-------
o3o3x3o3o . .   . ♦  20 |   90 |   60    60 |   15   30    15 |    6     6     0 | 1792    *    * |    4    0   0 |   4  0
. o3x3o3o3o .   . ♦  15 |   60 |   20    60 |    0   15    30 |    0     6     6 |    * 7168    * |    1    2   0 |   2  1
. . x3o3o3o3o   . ♦   6 |   15 |    0    20 |    0    0    15 |    0     0     6 |    *    * 7168 |    0    2   1 |   1  2
------------------+-----+------+------------+-----------------+------------------+----------------+---------------+-------
o3o3x3o3o3o .   . ♦  35 |  210 |  140   210 |   35  105   105 |   21    42    21 |    7    7    0 | 1024    *   * |   2  0
. o3x3o3o3o3o   . ♦  21 |  105 |   35   140 |    0   35   105 |    0    21    42 |    0    7    7 |    * 2048   * |   1  1
. . x3o3o3o3o4/3o ♦  12 |   60 |    0   160 |    0    0   240 |    0     0   192 |    0    0   64 |    *    * 112 |   0  2
------------------+-----+------+------------+-----------------+------------------+----------------+---------------+-------
o3o3x3o3o3o3o   . ♦  56 |  420 |  280   560 |   70  280   420 |   56   168   168 |   28   56   28 |    8    8   0 | 256  *
. o3x3o3o3o3o4/3o ♦  84 |  840 |  280  2240 |    0  560  3360 |    0   672  2688 |    0  448  896 |    0  128  14 |   * 16

o3o3o *b3o3o3x3o3o

. . .    . . . . . | 448 ♦   30 |   120   30 |   240  120   10 |   240   240   40 |   48   48  240   80 |   3   48   48   80 |  3  16  16
-------------------+-----+------+------------+-----------------+------------------+---------------------+--------------------+-----------
. . .    . . x . . |   2 | 6720 |     8    3 |    24   16    1 |    32    48    8 |    8    8   64   24 |   1   16   16   32 |  2   8   8
-------------------+-----+------+------------+-----------------+------------------+---------------------+--------------------+-----------
. . .    . o3x . . |   3 |    3 | 17920    * |     6    2    0 |    12    12    1 |    4    4   24    6 |   1    8    8   12 |  2   4   4
. . .    . . x3o . |   3 |    3 |     * 4480 |     0    8    1 |     0    24    8 |    0    0   32   24 |   0    8    8   32 |  1   8   8
-------------------+-----+------+------------+-----------------+------------------+---------------------+--------------------+-----------
. . .    o3o3x . . ♦   4 |    6 |     4    0 | 26880    *    * |     4     2    0 |    2    2    8    1 |   1    4    4    4 |  2   2   2
. . .    . o3x3o . ♦   6 |   12 |     4    4 |     * 8960    * |     0     6    1 |    0    0   12    6 |   0    4    4   12 |  1   4   4
. . .    . . x3o3o ♦   4 |    6 |     0    4 |     *    * 1120 ♦     0     0    8 |    0    0    0   24 |   0    0    0   32 |  0   8   8
-------------------+-----+------+------------+-----------------+------------------+---------------------+--------------------+-----------
. o . *b3o3o3x . . ♦   5 |   10 |    10    0 |     5    0    0 | 21504     *    * |    1    1    2    0 |   1    2    2    1 |  2   1   1
. . .    o3o3x3o . ♦  10 |   30 |    20   10 |     5    5    0 |     * 10752    * |    0    0    4    1 |   0    2    2    4 |  1   2   2
. . .    . o3x3o3o ♦  10 |   30 |    10   20 |     0    5    5 |     *     * 1792 ♦    0    0    0    6 |   0    0    0   12 |  0   4   4
-------------------+-----+------+------------+-----------------+------------------+---------------------+--------------------+-----------
o3o . *b3o3o3x . . ♦   6 |   15 |    20    0 |    15    0    0 |     6     0    0 | 3584    *    *    * |   1    2    0    0 |  2   1   0
. o3o *b3o3o3x . . ♦   6 |   15 |    20    0 |    15    0    0 |     6     0    0 |    * 3584    *    * |   1    0    2    0 |  2   0   1
. o . *b3o3o3x3o . ♦  15 |   60 |    60   20 |    30   15    0 |     6     6    0 |    *    * 7168    * |   0    1    1    1 |  1   1   1
. . .    o3o3x3o3o ♦  20 |   90 |    60   60 |    15   30   15 |     0     6    6 |    *    *    * 1792 |   0    0    0    4 |  0   2   2
-------------------+-----+------+------------+-----------------+------------------+---------------------+--------------------+-----------
o3o3o *b3o3o3x . . ♦  12 |   60 |   160    0 |   240    0    0 |   192     0    0 |   32   32    0    0 | 112    *    *    * |  2   0   0
o3o . *b3o3o3x3o . ♦  21 |  105 |   140   35 |   105   35    0 |    42    21    0 |    7    0    7    0 |   * 1024    *    * |  1   1   0
. o3o *b3o3o3x3o . ♦  21 |  105 |   140   35 |   105   35    0 |    42    21    0 |    0    7    7    0 |   *    * 1024    * |  1   0   1
. o . *b3o3o3x3o3o ♦  35 |  210 |   210  140 |   105  105   35 |    21    42   21 |    0    0    7    7 |   *    *    * 1024 |  0   1   1
-------------------+-----+------+------------+-----------------+------------------+---------------------+--------------------+-----------
o3o3o *b3o3o3x3o . ♦  84 |  840 |  2240  280 |  3360  560    0 |  2688   672    0 |  448  448  448    0 |  14   64   64    0 | 16   *   *
o3o . *b3o3o3x3o3o ♦  56 |  420 |   560  280 |   420  280   70 |   168   168   56 |   28    0   56   28 |   0    8    0    8 |  * 128   *
. o3o *b3o3o3x3o3o ♦  56 |  420 |   560  280 |   420  280   70 |   168   168   56 |    0   28   56   28 |   0    0    8    8 |  *   * 128

ooo3xox3oxo3ooo3ooo3ooo4ooo&#xt   → both heights = 1/sqrt(2) = 0.707107
(rez || pseudo barz || rez)

... 

qo oo3xo3ox3oo3oo3oo4oo&#zx   → height = 0
(tegum sum of q-height rez prism and equatorial barz)

...