As abstract polytope qro is isomorphic to soro, thereby replacing querco by sirco, qrit by srit, quarn by sirn, qrax by srox, and quersa by sersa. – As such qro is a lieutenant.

Incidence matrix according to Dynkin symbol

o3o3o3o3o3x3o4/3x

. . . . . . .   . | 7168 |    12    2 |    30     6    12    1 |    40    15    30    6 |    30    20    40   15 |    12   15    30  20 |    2    6   12  15 |   1    2  6
------------------+------+------------+------------------------+------------------------+------------------------+----------------------+--------------------+------------
. . . . . x .   . |    2 | 43008    * |     5     1     1    0 |    10     5     5    1 |    10    10    10    5 |     5   10    10  10 |    1    5    5  10 |   1    1  5
. . . . . . .   x |    2 |     * 7168 |     0     0     6    1 |     0     0    15    6 |     0     0    20   15 |     0    0    15  20 |    0    0    6  15 |   0    1  6
------------------+------+------------+------------------------+------------------------+------------------------+----------------------+--------------------+------------
. . . . o3x .   . |    3 |     3    0 | 71680     *     *    * |     4     1     1    0 |     6     4     4    1 |     4    6     6   4 |    1    4    4   6 |   1    1  4
. . . . . x3o   . |    3 |     3    0 |     * 14336     *    * |     0     5     0    1 |     0    10     0    5 |     0   10     0  10 |    0    5    0  10 |   1    0  5
. . . . . x .   x |    4 |     2    2 |     *     * 21504    * |     0     0     5    1 |     0     0    10    5 |     0    0    10  10 |    0    0    5  10 |   0    1  5
. . . . . . o4/3x |    4 |     0    4 |     *     *     * 1792 |     0     0     0    6 |     0     0     0   15 |     0    0     0  20 |    0    0    0  15 |   0    0  6
------------------+------+------------+------------------------+------------------------+------------------------+----------------------+--------------------+------------
. . . o3o3x .   . ♦    4 |     6    0 |     4     0     0    0 | 71680     *     *    * |     3     1     1    0 |     3    3     3   1 |    1    3    3   3 |   1    1  3
. . . . o3x3o   . ♦    6 |    12    0 |     4     4     0    0 |     * 17920     *    * |     0     4     0    1 |     0    6     0   4 |    0    4    0   6 |   1    0  4
. . . . o3x .   x ♦    6 |     6    3 |     2     0     3    0 |     *     * 35840    * |     0     0     4    1 |     0    0     6   4 |    0    0    4   6 |   0    1  4
. . . . . x3o4/3x ♦   24 |    24   24 |     0     8    12    6 |     *     *     * 1792 |     0     0     0    5 |     0    0     0  10 |    0    0    0  10 |   0    0  5
------------------+------+------------+------------------------+------------------------+------------------------+----------------------+--------------------+------------
. . o3o3o3x .   . ♦    5 |    10    0 |    10     0     0    0 |     5     0     0    0 | 43008     *     *    * |     2    1     1   0 |    1    2    2   1 |   1    1  2
. . . o3o3x3o   . ♦   10 |    30    0 |    20    10     0    0 |     5     5     0    0 |     * 14336     *    * |     0    3     0   1 |    0    3    0   3 |   1    0  3
. . . o3o3x .   x ♦    8 |    12    4 |     8     0     6    0 |     2     0     4    0 |     *     * 35840    * |     0    0     3   1 |    0    0    3   3 |   0    1  3
. . . . o3x3o4/3x ♦   96 |   192   96 |    64    64    96   24 |     0    16    32    8 |     *     *     * 1120 |     0    0     0   4 |    0    0    0   6 |   0    0  4
------------------+------+------------+------------------------+------------------------+------------------------+----------------------+--------------------+------------
. o3o3o3o3x .   . ♦    6 |    15    0 |    20     0     0    0 |    15     0     0    0 |     6     0     0    0 | 14336    *     *   * |    1    1    1   0 |   1    1  1
. . o3o3o3x3o   . ♦   15 |    60    0 |    60    20     0    0 |    30    15     0    0 |     6     6     0    0 |     * 7168     *   * |    0    2    0   1 |   1    0  2
. . o3o3o3x .   x ♦   10 |    20    5 |    20     0    10    0 |    10     0    10    0 |     2     0     5    0 |     *    * 21504   * |    0    0    2   1 |   0    1  2
. . . o3o3x3o4/3x ♦  320 |   960  320 |   640   320   480   80 |   160   160   320   40 |     0    32    80   10 |     *    *     * 448 |    0    0    0   3 |   0    0  3
------------------+------+------------+------------------------+------------------------+------------------------+----------------------+--------------------+------------
o3o3o3o3o3x .   . ♦    7 |    21    0 |    35     0     0    0 |    35     0     0    0 |    21     0     0    0 |     7    0     0   0 | 2048    *    *   * |   1    1  0
. o3o3o3o3x3o   . ♦   21 |   105    0 |   140    35     0    0 |   105    35     0    0 |    42    21     0    0 |     7    7     0   0 |    * 2048    *   * |   1    0  1
. o3o3o3o3x .   x ♦   12 |    30    6 |    40     0    15    0 |    30     0    20    0 |    12     0    15    0 |     2    0     6   0 |    *    * 7168   * |   0    1  1
. . o3o3o3x3o4/3x ♦  960 |  3840  960 |  3840  1280  1920  240 |  1920   960  1920  160 |   384   384   960   60 |     0   64   192  12 |    *    *    * 112 |   0    0  2
------------------+------+------------+------------------------+------------------------+------------------------+----------------------+--------------------+------------
o3o3o3o3o3x3o   . ♦   28 |   168    0 |   280    56     0    0 |   280    70     0    0 |   168    56     0    0 |    56   28     0   0 |    8    8    0   0 | 256    *  *
o3o3o3o3o3x .   x ♦   14 |    42    7 |    70     0    21    0 |    70     0    35    0 |    42     0    35    0 |    14    0    21   0 |    2    0    7   0 |   * 1024  *
. o3o3o3o3x3o4/3x ♦ 2688 | 13440 2688 | 17920  4480  6720  672 | 13440  4480  8960  560 |  5376  2688  6720  280 |   896  896  2688  84 |    0  128  448  14 |   *    * 16