ico+gico+24co

Acronym	...
Name	ico+gico+24co (?)
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 gico Grünbaumian relatives: ico+gico+72{4} general polytopal classes: Wythoffian polychora

Looks like a compound of an icositetrachoron (ico) with the compound of 3 vertex-inscribed tesseracts (tes, i.e. the great icositetrachoron, gico). Cells are connected by further 24 diametral co. Its vertex figure is a variation of querco, in fact q3o4/3x or q3/2o4x (which degenerates to something what looks like a cube plus an inscribed stella octangula (so), but diametral rectangles will there be in addition). Accordingly edges come in coincident triples, all faces come in coincident pairs, and the co also come in coincident pairs.

Incidence matrix according to Dynkin symbol

x3o4o3o4/3*a

. . . .      | 24 |  24 |  24  24 |  6 12  8
-------------+----+-----+---------+---------
x . . .      |  2 | 288 |   2   2 |  1  2  1
-------------+----+-----+---------+---------
x3o . .      |  3 |   3 | 192   * |  1  1  0
x . . o4/3*a |  4 |   4 |   * 144 |  0  1  1
-------------+----+-----+---------+---------
x3o4o .      ♦  6 |  12 |   8   0 | 24  *  *
x3o . o4/3*a ♦ 12 |  24 |   8   6 |  * 24  *
x . o3o4/3*a ♦  8 |  12 |   0   6 |  *  * 24

x3o4o3/2o4*a

. . .   .    | 24 |  24 |  24  24 |  6 12  8
-------------+----+-----+---------+---------
x . .   .    |  2 | 288 |   2   2 |  1  2  1
-------------+----+-----+---------+---------
x3o .   .    |  3 |   3 | 192   * |  1  1  0
x . .   o4*a |  4 |   4 |   * 144 |  0  1  1
-------------+----+-----+---------+---------
x3o4o   .    ♦  6 |  12 |   8   0 | 24  *  *
x3o .   o4*a ♦ 12 |  24 |   8   6 |  * 24  *
x . o3/2o4*a ♦  8 |  12 |   0   6 |  *  * 24

x3o4/3o3o4*a

. .   . .    | 24 |  24 |  24  24 |  6 12  8
-------------+----+-----+---------+---------
x .   . .    |  2 | 288 |   2   2 |  1  2  1
-------------+----+-----+---------+---------
x3o   . .    |  3 |   3 | 192   * |  1  1  0
x .   . o4*a |  4 |   4 |   * 144 |  0  1  1
-------------+----+-----+---------+---------
x3o4/3o .    ♦  6 |  12 |   8   0 | 24  *  *
x3o   . o4*a ♦ 12 |  24 |   8   6 |  * 24  *
x .   o3o4*a ♦  8 |  12 |   0   6 |  *  * 24

x3/2o4o3o4*a

.   . . .    | 24 |  24 |  24  24 |  6 12  8
-------------+----+-----+---------+---------
x   . . .    |  2 | 288 |   2   2 |  1  2  1
-------------+----+-----+---------+---------
x3/2o . .    |  3 |   3 | 192   * |  1  1  0
x   . . o4*a |  4 |   4 |   * 144 |  0  1  1
-------------+----+-----+---------+---------
x3/2o4o .    ♦  6 |  12 |   8   0 | 24  *  *
x3/2o . o4*a ♦ 12 |  24 |   8   6 |  * 24  *
x   . o3o4*a ♦  8 |  12 |   0   6 |  *  * 24

x3o4/3o3/2o4/3*a

. .   .   .      | 24 |  24 |  24  24 |  6 12  8
-----------------+----+-----+---------+---------
x .   .   .      |  2 | 288 |   2   2 |  1  2  1
-----------------+----+-----+---------+---------
x3o   .   .      |  3 |   3 | 192   * |  1  1  0
x .   .   o4/3*a |  4 |   4 |   * 144 |  0  1  1
-----------------+----+-----+---------+---------
x3o4/3o   .      ♦  6 |  12 |   8   0 | 24  *  *
x3o   .   o4/3*a ♦ 12 |  24 |   8   6 |  * 24  *
x .   o3/2o4/3*a ♦  8 |  12 |   0   6 |  *  * 24

x3/2o4o3/2o4/3*a

.   . .   .      | 24 |  24 |  24  24 |  6 12  8
-----------------+----+-----+---------+---------
x   . .   .      |  2 | 288 |   2   2 |  1  2  1
-----------------+----+-----+---------+---------
x3/2o .   .      |  3 |   3 | 192   * |  1  1  0
x   . .   o4/3*a |  4 |   4 |   * 144 |  0  1  1
-----------------+----+-----+---------+---------
x3/2o4o   .      ♦  6 |  12 |   8   0 | 24  *  *
x3/2o .   o4/3*a ♦ 12 |  24 |   8   6 |  * 24  *
x   . o3/2o4/3*a ♦  8 |  12 |   0   6 |  *  * 24

x3/2o4/3o3o4/3*a

.   .   . .      | 24 |  24 |  24  24 |  6 12  8
-----------------+----+-----+---------+---------
x   .   . .      |  2 | 288 |   2   2 |  1  2  1
-----------------+----+-----+---------+---------
x3/2o   . .      |  3 |   3 | 192   * |  1  1  0
x   .   . o4/3*a |  4 |   4 |   * 144 |  0  1  1
-----------------+----+-----+---------+---------
x3/2o4/3o .      ♦  6 |  12 |   8   0 | 24  *  *
x3/2o   . o4/3*a ♦ 12 |  24 |   8   6 |  * 24  *
x   .   o3o4/3*a ♦  8 |  12 |   0   6 |  *  * 24

x3/2o4/3o3/2o4*a

.   .   .   .    | 24 |  24 |  24  24 |  6 12  8
-----------------+----+-----+---------+---------
x   .   .   .    |  2 | 288 |   2   2 |  1  2  1
-----------------+----+-----+---------+---------
x3/2o   .   .    |  3 |   3 | 192   * |  1  1  0
x   .   .   o4*a |  4 |   4 |   * 144 |  0  1  1
-----------------+----+-----+---------+---------
x3/2o4/3o   .    ♦  6 |  12 |   8   0 | 24  *  *
x3/2o   .   o4*a ♦ 12 |  24 |   8   6 |  * 24  *
x   .   o3/2o4*a ♦  8 |  12 |   0   6 |  *  * 24

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