Acronym ...
Name β3x4x3β (?)
Circumradius ...

No uniform realisation is possible.


Incidence matrix according to Dynkin symbol

β3x4x3β

both( . . . .    ) | 1152 |   1   1   1   1   1 |   1   1   1   1   2   2   1 |  1  1  1  1   2
-------------------+------+---------------------+-----------------------------+----------------
both( . x . .    ) |    2 | 576   *   *   *   * |   1   1   0   0   1   0   1 |  1  1  0  1   1
both( . . x .    ) |    2 |   * 576   *   *   * |   1   0   1   1   0   1   0 |  1  0  1  1   1
both( s . . s2*a ) |    2 |   *   * 576   *   * |   0   0   0   0   2   2   0 |  0  1  1  0   2
sefa( β3x . .    ) |    2 |   *   *   * 576   * |   0   1   0   1   1   0   0 |  1  1  0  0   1
sefa( . . x3β    ) |    2 |   *   *   *   * 576 |   0   0   1   0   0   1   1 |  0  0  1  1   1
-------------------+------+---------------------+-----------------------------+----------------
both( . x4x .    ) |    8 |   4   4   0   0   0 | 144   *   *   *   *   *   * |  1  0  0  1   0
      β3x . .          6 |   3   0   0   3   0 |   * 192   *   *   *   *   * |  1  1  0  0   0
      . . x3β          6 |   0   3   0   0   3 |   *   * 192   *   *   *   * |  0  0  1  1   0
sefa( β3x4x .    ) |    8 |   0   4   0   4   0 |   *   *   * 144   *   *   * |  1  0  0  0   1
sefa( β3x . β2*a ) |    4 |   1   0   2   1   0 |   *   *   *   * 576   *   * |  0  1  0  0   1
sefa( β . x3β2*a ) |    4 |   0   1   2   0   1 |   *   *   *   *   * 576   * |  0  0  1  0   1
sefa( . x4x3β    ) |    8 |   4   0   0   0   4 |   *   *   *   *   *   * 144 |  0  0  0  1   1
-------------------+------+---------------------+-----------------------------+----------------
      β3x4x .         48 |  24  24   0  24   0 |   6   8   0   6   0   0   0 | 24  *  *  *   *
      β3x . β2*a      12 |   6   0   6   6   0 |   0   2   0   0   6   0   0 |  * 96  *  *   *
      β . x3β2*a      12 |   0   6   6   0   6 |   0   0   2   0   0   6   0 |  *  * 96  *   *
      . x4x3β         48 |  24  24   0   0  24 |   6   0   8   0   0   0   6 |  *  *  * 24   *
sefa( β3x4x3β    )    16 |   4   4   8   4   4 |   0   0   0   1   4   4   1 |  *  *  *  * 144
or
both( . . . .    )    | 1152 |    2   1    2 |   1   2   2    4 |  2   2   2
----------------------+------+---------------+------------------+-----------
both( . x . .    )  & |    2 | 1152   *    * |   1   1   1    1 |  2   1   1
both( s . . s2*a )    |    2 |    * 576    * |   0   0   0    4 |  0   2   2
sefa( β3x . .    )  & |    2 |    *   * 1152 |   0   1   1    1 |  1   1   1
----------------------+------+---------------+------------------+-----------
both( . x4x .    )    |    8 |    8   0    0 | 144   *   *    * |  2   0   0
      β3x . .       &     6 |    3   0    3 |   * 384   *    * |  1   1   0
sefa( β3x4x .    )  & |    8 |    4   0    4 |   *   * 288    * |  1   0   1
sefa( β3x . β2*a )  & |    4 |    1   2    1 |   *   *   * 1152 |  0   1   1
----------------------+------+---------------+------------------+-----------
      β3x4x .       &    48 |   48   0   24 |   6   8   6    0 | 48   *   *
      β3x . β2*a    &    12 |    6   6    6 |   0   2   0    6 |  * 192   *
sefa( β3x4x3β    )       16 |    8   8    8 |   0   0   2    8 |  *   * 144

starting figure: x3x4x3x

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