Acronym broc (old: droc)
Name birectified octaexon,
duorectified octaexon,
vertex figure of bif,
Gosset polytope 04,2
Circumradius sqrt(15)/4 = 0.968246
Confer
general polytopal classes:
segmentoexa   fundamental lace prisms   Coxeter-Elte-Gosset polytopes  
External
links
wikipedia  

Incidence matrix according to Dynkin symbol

o3o3x3o3o3o3o

. . . . . . . | 56   15 |  15  30 |  5  30  30 | 10  30  15 | 10 15  3 | 5 3
--------------+----+-----+---------+------------+------------+----------+----
. . x . . . . |  2 | 420 |   2   4 |  1   8   6 |  4  12   4 |  6  8  1 | 4 2
--------------+----+-----+---------+------------+------------+----------+----
. o3x . . . . |  3 |   3 | 280   * |  1   4   0 |  4   6   0 |  6  4  0 | 4 1
. . x3o . . . |  3 |   3 |   * 560 |  0   2   3 |  1   6   3 |  3  6  1 | 3 2
--------------+----+-----+---------+------------+------------+----------+----
o3o3x . . . .   4 |   6 |   4   0 | 70   *   *   4   0   0 |  6  0  0 | 4 0
. o3x3o . . .   6 |  12 |   4   4 |  * 280   * |  1   3   0 |  3  3  0 | 3 1
. . x3o3o . .   4 |   6 |   0   4 |  *   * 420 |  0   2   2 |  1  4  1 | 2 2
--------------+----+-----+---------+------------+------------+----------+----
o3o3x3o . . .  10 |  30 |  20  10 |  5   5   0 | 56   *   * |  3  0  0 | 3 0
. o3x3o3o . .  10 |  30 |  10  20 |  0   5   5 |  * 168   * |  1  2  0 | 2 1
. . x3o3o3o .   5 |  10 |   0  10 |  0   0   5 |  *   * 168 |  0  2  1 | 1 2
--------------+----+-----+---------+------------+------------+----------+----
o3o3x3o3o . .  20 |  90 |  60  60 | 15  30  15 |  6   6   0 | 28  *  * | 2 0
. o3x3o3o3o .  15 |  60 |  20  60 |  0  15  30 |  0   6   6 |  * 56  * | 1 1
. . x3o3o3o3o   6 |  15 |   0  20 |  0   0  15 |  0   0   6 |  *  * 28 | 0 2
--------------+----+-----+---------+------------+------------+----------+----
o3o3x3o3o3o .  35 | 210 | 140 210 | 35 105 105 | 21  42  21 |  7  7  0 | 8 *
. o3x3o3o3o3o  21 | 105 |  35 140 |  0  35 105 |  0  21  42 |  0  7  7 | * 8

oo3xo3ox3oo3oo3oo&#x   → height = 2/sqrt(7) = 0.755929
(ril || bril)

o.3o.3o.3o.3o.3o.    | 21  *   10   5   0 |  5  20  10  10   0   0 | 10  20  5  20  10  0   0   0 | 10 10 10  20   5  0  0  0 | 5 2 10 10  1 0 0 | 1 5 2 0
.o3.o3.o3.o3.o3.o    |  * 35    0   3  12 |  0   0   3  12  12  18 |  0   0  1  12  18  4  18  12 |  0  0  4  18  12  6 12  3 | 0 0  6 12  3 4 3 | 0 4 3 1
---------------------+-------+-------------+------------------------+------------------------------+---------------------------+------------------+--------
.. x. .. .. .. ..    |  2  0 | 105   *   * |  1   4   1   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
oo3oo3oo3oo3oo3oo&#x |  1  1 |   * 105   * |  0   0   2   4   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
.. .. .x .. .. ..    |  0  2 |   *   * 210 |  0   0   0   1   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. .. .. .. ..    |  3  0 |   3   0   0 | 35   *   *   *   *   * |  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. .. .. ..    |  3  0 |   3   0   0 |  * 140   *   *   *   * |  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
.. xo .. .. .. ..&#x |  2  1 |   1   2   0 |  *   * 105   *   *   * |  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
.. .. ox .. .. ..&#x |  1  2 |   0   2   1 |  *   *   * 210   *   * |  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.x .. .. ..    |  0  3 |   0   0   3 |  *   *   *   * 140   * |  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.o .. ..    |  0  3 |   0   0   3 |  *   *   *   *   * 210 |  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. .. .. ..      6  0 |  12   0   0 |  4   4   0   0   0   0 | 35   *  *   *   *  *   *   * |  3  0  1   0   0  0  0  0 | 3 0  3  0  0 0 0 | 1 3 0 0
.. x.3o.3o. .. ..      4  0 |   6   0   0 |  0   4   0   0   0   0 |  * 105  *   *   *  *   *   * |  1  2  0   1   0  0  0  0 | 2 1  1  2  0 0 0 | 1 2 1 0
oo3xo .. .. .. ..&#x   3  1 |   3   3   0 |  1   0   3   0   0   0 |  *   * 35   *   *  *   *   *   0  0  4   0   0  0  0  0 | 0 0  6  0  0 0 0 | 0 4 0 0
.. xo3ox .. .. ..&#x   3  3 |   3   6   3 |  0   1   3   3   1   0 |  *   *  * 140   *  *   *   * |  0  0  1   3   0  0  0  0 | 0 0  3  3  0 0 0 | 0 3 1 0
.. .. ox3oo .. ..&#x   1  3 |   0   3   3 |  0   0   0   3   0   1 |  *   *  *   * 210  *   *   * |  0  0  0   2   2  0  0  0 | 0 0  1  4  1 0 0 | 0 2 2 0
.o3.o3.x .. .. ..      0  4 |   0   0   6 |  0   0   0   0   4   0 |  *   *  *   *   * 35   *   *   0  0  1   0   0  3  0  0 | 0 0  3  0  0 3 0 | 0 3 0 1
.. .o3.x3.o .. ..      0  6 |   0   0  12 |  0   0   0   0   4   4 |  *   *  *   *   *  * 105   * |  0  0  0   1   0  1  2  0 | 0 0  1  2  0 2 1 | 0 2 1 1
.. .. .x3.o3.o ..      0  4 |   0   0   6 |  0   0   0   0   0   4 |  *   *  *   *   *  *   * 105 |  0  0  0   0   1  0  2  1 | 0 0  0  2  1 1 2 | 0 1 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 | 21  *  *   *   *  *  *  * | 2 0  1  0  0 0 0 | 1 2 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 |  * 42  *   *   *  *  *  * | 1 1  0  1  0 0 0 | 1 1 1 0
oo3xo3ox .. .. ..&#x   6  4 |  12  12   6 |  4   4  12   6   4   0 |  1   0  4   4   0  1   0   0 |  *  * 35   *   *  *  *  * | 0 0  3  0  0 0 0 | 0 3 0 0
.. xo3ox3oo .. ..&#x   4  6 |   6  12  12 |  0   4   6  12   4   4 |  0   1  0   4   4  0   1   0 |  *  *  * 105   *  *  *  * | 0 0  1  2  0 0 0 | 0 2 1 0
.. .. ox3oo3oo ..&#x   1  4 |   0   4   6 |  0   0   0   6   0   4 |  0   0  0   0   4  0   0   1 |  *  *  *   * 105  *  *  * | 0 0  0  2  1 0 0 | 0 1 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 |  *  *  *   *   * 21  *  * | 0 0  1  0  0 2 0 | 0 2 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 |  *  *  *   *   *  * 42  * | 0 0  0  1  0 1 1 | 0 1 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 |  *  *  *   *   *  *  * 21 | 0 0  0  0  1 0 2 | 0 0 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 | 7 *  *  *  * * * | 1 1 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 | * 7  *  *  * * * | 1 0 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 | * * 21  *  * * * | 0 2 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 | * *  * 42  * * * | 0 1 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 | * *  *  * 21 * * | 0 0 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 | * *  *  *  * 7 * | 0 1 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 | * *  *  *  * * 7 | 0 0 1 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 | 1 * * *
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 | * 7 * *
.. 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 | * * 7 *
.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 | * * * 1

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