Acronym ...
Name 2ico+2gico (?)
Circumradius 1
General of army ico
Colonel of regiment ico
Confer
non-Grünbaumian master:
ico   tes  
Grünbaumian relatives:
2ico   2tes   ico+gico+72{4}  
compounds:
gico  

Looks like a vertex-coincident compound of 2 icositetrachora (ico) and 6 tesseracts (tes). – The latter part itself can be looked at either as a compound of 3 Grünbaumian double covered tesseracts (2tes) or as a double cover of 2 great icositetrachora (gico).

Its vertex figure is a 2quith variant, where the {6/2}-edges are of size q. That one in turn looks like a double cover of a figure which is a vertex-coincident compound of a cube and a q-scaled stella octangula (so, i.e. the regular compound of 2 tet).


Incidence matrix according to Dynkin symbol

x4o4o4o4*a3/2*c *b3/2*d

. . . .                 | 24 |  48 |  24  24  24 |  6  8  6
------------------------+----+-----+-------------+---------
x . . .                 |  2 | 576 |   1   1   1 |  1  1  1
------------------------+----+-----+-------------+---------
x4o . .                 |  4 |   4 | 144   *   * |  1  1  0
x . o . *a3/2*c         |  3 |   3 |   * 192   * |  1  0  1
x . . o4*a              |  4 |   4 |   *   * 144 |  0  1  1
------------------------+----+-----+-------------+---------
x4o4o . *a3/2*c           6 |  24 |   6   8   0 | 24  *  *
x4o . o4*a      *b3/2*d   8 |  24 |   6   0   6 |  * 24  *
x . o4o4*a3/2*c           6 |  24 |   0   8   6 |  *  * 24
or
. . . .                   | 24 |  48 |  48  24 | 12  8
--------------------------+----+-----+---------+------
x . . .                   |  2 | 576 |   2   1 |  2  1
--------------------------+----+-----+---------+------
x4o . .                 & |  4 |   4 | 288   * |  1  1
x . o . *a3/2*c           |  3 |   3 |   * 192 |  2  0
--------------------------+----+-----+---------+------
x4o4o . *a3/2*c         &   6 |  24 |   6   8 | 48  *
x4o . o4*a      *b3/2*d     8 |  24 |  12   0 |  * 24

x4o4o4/3o4/3*a3/2*c *b3*d

. . .   .                 | 24 |  48 |  24  24  24 |  6  8  6
--------------------------+----+-----+-------------+---------
x . .   .                 |  2 | 576 |   1   1   1 |  1  1  1
--------------------------+----+-----+-------------+---------
x4o .   .                 |  4 |   4 | 144   *   * |  1  1  0
x . o   .   *a3/2*c       |  3 |   3 |   * 192   * |  1  0  1
x . .   o4/3*a            |  4 |   4 |   *   * 144 |  0  1  1
--------------------------+----+-----+-------------+---------
x4o4o   .   *a3/2*c         6 |  24 |   6   8   0 | 24  *  *
x4o .   o4/3*a      *b3*d   8 |  24 |   6   0   6 |  * 24  *
x . o4/3o4/3*a3/2*c         6 |  24 |   0   8   6 |  *  * 24

x4o4/3o4o4/3*a3*c *b3*d

. .   . .               | 24 |  48 |  24  24  24 |  6  8  6
------------------------+----+-----+-------------+---------
x .   . .               |  2 | 576 |   1   1   1 |  1  1  1
------------------------+----+-----+-------------+---------
x4o   . .               |  4 |   4 | 144   *   * |  1  1  0
x .   o .   *a3*c       |  3 |   3 |   * 192   * |  1  0  1
x .   . o4/3*a          |  4 |   4 |   *   * 144 |  0  1  1
------------------------+----+-----+-------------+---------
x4o4/3o .   *a3*c         6 |  24 |   6   8   0 | 24  *  *
x4o   . o4/3*a    *b3*d   8 |  24 |   6   0   6 |  * 24  *
x .   o4o4/3*a3*c         6 |  24 |   0   8   6 |  *  * 24

x4o4/3o4/3o4*a3*c *b3/2*d

. .   .   .               | 24 |  48 |  24  24  24 |  6  8  6
--------------------------+----+-----+-------------+---------
x .   .   .               |  2 | 576 |   1   1   1 |  1  1  1
--------------------------+----+-----+-------------+---------
x4o   .   .               |  4 |   4 | 144   *   * |  1  1  0
x .   o   . *a3*c         |  3 |   3 |   * 192   * |  1  0  1
x .   .   o4*a            |  4 |   4 |   *   * 144 |  0  1  1
--------------------------+----+-----+-------------+---------
x4o4/3o   . *a3*c           6 |  24 |   6   8   0 | 24  *  *
x4o   .   o4*a    *b3/2*d   8 |  24 |   6   0   6 |  * 24  *
x .   o4/3o4*a3*c           6 |  24 |   0   8   6 |  *  * 24
or
. .   .   .                 | 24 |  48 |  48  24 | 12  8
----------------------------+----+-----+---------+------
x .   .   .                 |  2 | 576 |   2   1 |  2  1
----------------------------+----+-----+---------+------
x4o   .   .               & |  4 |   4 | 288   * |  1  1
x .   o   . *a3*c           |  3 |   3 |   * 192 |  2  0
----------------------------+----+-----+---------+------
x4o4/3o   . *a3*c         &   6 |  24 |   6   8 | 48  *
x4o   .   o4*a    *b3/2*d     8 |  24 |  12   0 |  * 24

x4/3o4o4o4/3*a3*c *b3/2*d

.   . . .                 | 24 |  48 |  24  24  24 |  6  8  6
--------------------------+----+-----+-------------+---------
x   . . .                 |  2 | 576 |   1   1   1 |  1  1  1
--------------------------+----+-----+-------------+---------
x4/3o . .                 |  4 |   4 | 144   *   * |  1  1  0
x   . o .   *a3*c         |  3 |   3 |   * 192   * |  1  0  1
x   . . o4/3*a            |  4 |   4 |   *   * 144 |  0  1  1
--------------------------+----+-----+-------------+---------
x4/3o4o .   *a3*c           6 |  24 |   6   8   0 | 24  *  *
x4/3o . o4/3*a    *b3/2*d   8 |  24 |   6   0   6 |  * 24  *
x   . o4o4/3*a3*c           6 |  24 |   0   8   6 |  *  * 24
or
.   . . .                   | 24 |  48 |  48  24 | 12  8
----------------------------+----+-----+---------+------
x   . . .                   |  2 | 576 |   2   1 |  2  1
----------------------------+----+-----+---------+------
x4/3o . .                 & |  4 |   4 | 288   * |  1  1
x   . o .   *a3*c           |  3 |   3 |   * 192 |  2  0
----------------------------+----+-----+---------+------
x4/3o4o .   *a3*c         &   6 |  24 |   6   8 | 48  *
x4/3o . o4/3*a    *b3/2*d     8 |  24 |  12   0 |  * 24

x4/3o4/3o4/3o4/3*a3/2*c *b3/2*d

.   .   .   .                   | 24 |  48 |  24  24  24 |  6  8  6
--------------------------------+----+-----+-------------+---------
x   .   .   .                   |  2 | 576 |   1   1   1 |  1  1  1
--------------------------------+----+-----+-------------+---------
x4/3o   .   .                   |  4 |   4 | 144   *   * |  1  1  0
x   .   o   .   *a3/2*c         |  3 |   3 |   * 192   * |  1  0  1
x   .   .   o4/3*a              |  4 |   4 |   *   * 144 |  0  1  1
--------------------------------+----+-----+-------------+---------
x4/3o4/3o   .   *a3/2*c           6 |  24 |   6   8   0 | 24  *  *
x4/3o   .   o4/3*a      *b3/2*d   8 |  24 |   6   0   6 |  * 24  *
x   .   o4/3o4/3*a3/2*c           6 |  24 |   0   8   6 |  *  * 24
or
.   .   .   .                     | 24 |  48 |  48  24 | 12  8
----------------------------------+----+-----+---------+------
x   .   .   .                     |  2 | 576 |   2   1 |  2  1
----------------------------------+----+-----+---------+------
x4/3o   .   .                   & |  4 |   4 | 288   * |  1  1
x   .   o   .   *a3/2*c           |  3 |   3 |   * 192 |  2  0
----------------------------------+----+-----+---------+------
x4/3o4/3o   .   *a3/2*c         &   6 |  24 |   6   8 | 48  *
x4/3o   .   o4/3*a      *b3/2*d     8 |  24 |  12   0 |  * 24

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