Acronym ...
Name 3ex+fix (?)
Circumradius (1+sqrt(5))/2 = 1.618034
General of army ex
Colonel of regiment ex
Confer
non-Grünbaumian masters:
ex   fix  
Grünbaumian relatives:
ex+fix   2ex   2ex+fix   3ex+2fix+gaghi   2fix  

Looks like a compound of 3 coincident exes with fix, and indeed the vertices coincide by four, edges coincide by six, {3}s by four, and tets by 3.


Incidence matrix according to Dynkin symbol

x3/2x3o5o

.   . . . | 1440 |   1    5 |    5    5 |   5   1
----------+------+----------+-----------+--------
x   . . . |    2 | 720    * |    5    0 |   5   0
.   x . . |    2 |   * 3600 |    1    2 |   2   1
----------+------+----------+-----------+--------
x3/2x . . |    6 |   3    3 | 1200    * |   2   0
.   x3o . |    3 |   0    3 |    * 2400 |   1   1
----------+------+----------+-----------+--------
x3/2x3o .    12 |   6   12 |    4    4 | 600   *
.   x3o5o    12 |   0   30 |    0   20 |   * 120

x3/2x3/2o5o

.   .   . . | 1440 |   1    5 |    5    5 |   5   1
------------+------+----------+-----------+--------
x   .   . . |    2 | 720    * |    5    0 |   5   0
.   x   . . |    2 |   * 3600 |    1    2 |   2   1
------------+------+----------+-----------+--------
x3/2x   . . |    6 |   3    3 | 1200    * |   2   0
.   x3/2o . |    3 |   0    3 |    * 2400 |   1   1
------------+------+----------+-----------+--------
x3/2x3/2o .    12 |   6   12 |    4    4 | 600   *
.   x3/2o5o    12 |   0   30 |    0   20 |   * 120

x3/2x3o5/4o

.   . .   . | 1440 |   1    5 |    5    5 |   5   1
------------+------+----------+-----------+--------
x   . .   . |    2 | 720    * |    5    0 |   5   0
.   x .   . |    2 |   * 3600 |    1    2 |   2   1
------------+------+----------+-----------+--------
x3/2x .   . |    6 |   3    3 | 1200    * |   2   0
.   x3o   . |    3 |   0    3 |    * 2400 |   1   1
------------+------+----------+-----------+--------
x3/2x3o   .    12 |   6   12 |    4    4 | 600   *
.   x3o5/4o    12 |   0   30 |    0   20 |   * 120

x3/2x3/2o5/4o

.   .   .   . | 1440 |   1    5 |    5    5 |   5   1
--------------+------+----------+-----------+--------
x   .   .   . |    2 | 720    * |    5    0 |   5   0
.   x   .   . |    2 |   * 3600 |    1    2 |   2   1
--------------+------+----------+-----------+--------
x3/2x   .   . |    6 |   3    3 | 1200    * |   2   0
.   x3/2o   . |    3 |   0    3 |    * 2400 |   1   1
--------------+------+----------+-----------+--------
x3/2x3/2o   .    12 |   6   12 |    4    4 | 600   *
.   x3/2o5/4o    12 |   0   30 |    0   20 |   * 120

(-x)3x3o5o

  .  . . . | 1440 |   1    5 |    5    5 |   5   1
-----------+------+----------+-----------+--------
 -x  . . . |    2 | 720    * |    5    0 |   5   0
  .  x . . |    2 |   * 3600 |    1    2 |   2   1
-----------+------+----------+-----------+--------
(-x)3x . . |    6 |   3    3 | 1200    * |   2   0
  .  x3o . |    3 |   0    3 |    * 2400 |   1   1
-----------+------+----------+-----------+--------
(-x)3x3o .    12 |   6   12 |    4    4 | 600   *
  .  x3o5o    12 |   0   30 |    0   20 |   * 120

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