2ico+2gico

Acronym	...
Name	2ico+2gico (?)
Circumradius	1
Coordinates	(1, 0, 0, 0) & all permutations, all changes of sign (vertex inscribed q-hex) (±1/2, ±1/2, ±1/2, ±1/2) & all permutations, even number of minus signs (vertex inscribed q-hex) (±1/2, ±1/2, ±1/2, ±1/2) & all permutations, odd number of minus signs (vertex inscribed q-hex) The hull of any pair of those sets describes a tesseracts.
General of army	ico
Colonel of regiment	ico
Confer	non-Grünbaumian master: ico tes Grünbaumian relatives: 2ico 2tes ico+gico+72{4} compounds: gico general polytopal classes: Wythoffian polychora

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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