Acronym ...
Name o3β3β4o (?)
Circumradius ...

No uniform realisation is possible.


Incidence matrix according to Dynkin symbol

o3β3β4o

both( . . . . ) | 96 |  1  2   8 |  1   4   6   6 |  2  2  4
----------------+----+-----------+----------------+---------
both( . . s4o ) |  2 | 48  *   * |  0   0   0   4 |  0  2  2
sefa( o3β . . ) |  2 |  * 96   * |  1   0   2   0 |  2  0  1
sefa( . s3s . ) |  2 |  *  * 384 |  0   1   1   1 |  1  1  1
----------------+----+-----------+----------------+---------
      o3β . .     3 |  0  3   0 | 32   *   *   * |  2  0  0
both( . s3s . )   3 |  0  0   3 |  * 128   *   * |  1  1  0
sefa( o3β3β . ) |  3 |  0  1   2 |  *   * 192   * |  1  0  1
sefa( . s3s4o ) |  3 |  1  0   2 |  *   *   * 192 |  0  1  1
----------------+----+-----------+----------------+---------
      o3β3β .    12 |  0 12  24 |  4   8  12   0 | 16  *  *
both( . s3s4o )  12 |  6  0  24 |  0   8   0  12 |  * 16  *
sefa( o3β3β4o )   4 |  1  1   4 |  0   0   2   2 |  *  * 96

starting figure: o3x3x4o

β3β3β *b3o

both( . . .    . ) | 96 |  1   4   4  2 |  2  2  1   6  3  3 |  2 1 1  4
-------------------+----+---------------+--------------------+----------
both( s 2 s    . ) |  2 | 48   *   *  * |  0  0  0   4  0  0 |  2 0 0  2
sefa( s3s .    . ) |  2 |  * 192   *  * |  1  0  0   1  1  0 |  1 1 0  1
sefa( . s3s    . ) |  2 |  *   * 192  * |  0  1  0   1  0  1 |  1 0 1  1
sefa( . β . *b3o ) |  2 |  *   *   * 96 |  0  0  1   0  1  1 |  0 1 1  1
-------------------+----+---------------+--------------------+----------
both( s3s .    . )   3 |  0   3   0  0 | 64  *  *   *  *  * |  1 1 0  0
both( . s3s    . )   3 |  0   0   3  0 |  * 64  *   *  *  * |  1 0 1  0
      . β . *b3o     3 |  0   0   0  3 |  *  * 32   *  *  * |  0 1 1  0
sefa( s3s3s    . ) |  3 |  1   1   1  0 |  *  *  * 192  *  * |  1 0 0  1
sefa( β3β . *b3o ) |  3 |  0   2   0  1 |  *  *  *   * 96  * |  0 1 0  1
sefa( . β3β *b3o ) |  3 |  0   0   2  1 |  *  *  *   *  * 96 |  0 0 1  1
-------------------+----+---------------+--------------------+----------
both( s3s3s    . )  12 |  6  12  12  0 |  4  4  0  12  0  0 | 16 * *  *
      β3β . *b3o    12 |  0  24   0 12 |  8  0  4   0 12  0 |  * 8 *  *
      . β3β *b3o    12 |  0   0  24 12 |  0  8  4   0  0 12 |  * * 8  *
sefa( β3β3β *b3o )   4 |  1   2   2  1 |  0  0  0   2  1  1 |  * * * 96

starting figure: x3x3x *b3o

© 2004-2019
top of page