Acronym ...
Name 2ico (?)
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  
Grünbaumian relatives:
2ico+2gico   2ico+48{4}+128{3}  
general polytopal classes:
Wythoffian polychora  

Comes in 2 different types. Both look like a compound of 2 coincident icositetrachora (ico). Type A uses Grünbaumian elements and all others are pairwise coincident. Type B identifies vertices and edges, but uses singly wrapped elements only (using a Grünbaumian vertex figure.


Incidence matrix according to Dynkin symbol

β3x3o4o   (Type A)

both( . . . . ) | 48 ♦  4  4 |  4  4  4 | 1  4 1
----------------+----+-------+----------+-------
both( . x . . ) |  2 | 96  * |  2  1  0 | 1  2 0
sefa( β3x . . ) |  2 |  * 96 |  0  1  2 | 0  2 1
----------------+----+-------+----------+-------
both( . x3o . ) |  3 |  3  0 | 64  *  * | 1  1 0
      β3x . .   ♦  6 |  3  3 |  * 32  * | 0  2 0
sefa( β3x3o . ) |  3 |  0  3 |  *  * 64 | 0  1 1
----------------+----+-------+----------+-------
both( . x3o4o ) ♦  6 | 12  0 |  8  0  0 | 8  * *
      β3x3o .   ♦ 12 | 12 12 |  4  4  4 | * 16 *
sefa( β3x3o4o ) ♦  6 |  0 12 |  0  0  8 | *  * 8

starting figure: x3x3o4o


β3x3o *b3o   (Type A)

both( . . .    . ) | 48 ♦  4  4 |  2  2  4  2  2 | 1 2 2 1
-------------------+----+-------+----------------+--------
both( . x .    . ) |  2 | 96  * |  1  1  1  0  0 | 1 1 1 0
sefa( β3x .    . ) |  2 |  * 96 |  0  0  1  1  1 | 0 1 1 1
-------------------+----+-------+----------------+--------
both( . x3o    . ) |  3 |  3  0 | 32  *  *  *  * | 1 1 0 0
both( . x . *b3o ) |  3 |  3  0 |  * 32  *  *  * | 1 0 1 0
      β3x .    .   ♦  6 |  3  3 |  *  * 32  *  * | 0 1 1 0
sefa( β3x3o    . ) |  3 |  0  3 |  *  *  * 32  * | 0 1 0 1
sefa( β3x . *b3o ) |  3 |  0  3 |  *  *  *  * 32 | 0 0 1 1
-------------------+----+-------+----------------+--------
both( . x3o *b3o ) ♦  6 | 12  0 |  4  4  0  0  0 | 8 * * *
      β3x3o    .   ♦ 12 | 12 12 |  4  0  4  4  0 | * 8 * *
      β3x . *b3o   ♦ 12 | 12 12 |  0  4  4  0  4 | * * 8 *
sefa( β3x3o *b3o ) ♦  6 |  0 12 |  0  0  0  4  4 | * * * 8

starting figure: x3x3o *b3o


x3o4o3o4/3*b   (Type B)

. . . .      | 24 ♦  8 |  24 |  6  6
-------------+----+----+-----+------
x . . .      |  2 | 96 |   6 |  3  3
-------------+----+----+-----+------
x3o . .      |  3 |  3 | 192 |  1  1
-------------+----+----+-----+------
x3o4o .      ♦  6 | 12 |   8 | 24  *
x3o . o4/3*b ♦  6 | 12 |   8 |  * 24


x3o4o3/2o4*b   (Type B)

. . .   .    | 24 ♦  8 |  24 |  6  6
-------------+----+----+-----+------
x . .   .    |  2 | 96 |   6 |  3  3
-------------+----+----+-----+------
x3o .   .    |  3 |  3 | 192 |  1  1
-------------+----+----+-----+------
x3o4o   .    ♦  6 | 12 |   8 | 24  *
x3o .   o4*b ♦  6 | 12 |   8 |  * 24

or
. . .   .       | 24 ♦  8 |  24 | 12
----------------+----+----+-----+---
x . .   .       |  2 | 96 |   6 |  6
----------------+----+----+-----+---
x3o .   .       |  3 |  3 | 192 |  2
----------------+----+----+-----+---
x3o4o   .     & ♦  6 | 12 |   8 | 48


x3o4/3o3/2o4/3*b   (Type B)

. .   .   .      | 24 ♦  8 |  24 |  6  6
-----------------+----+----+-----+------
x .   .   .      |  2 | 96 |   6 |  3  3
-----------------+----+----+-----+------
x3o   .   .      |  3 |  3 | 192 |  1  1
-----------------+----+----+-----+------
x3o4/3o   .      ♦  6 | 12 |   8 | 24  *
x3o   .   o4/3*b ♦  6 | 12 |   8 |  * 24

or
. .   .   .         | 24 ♦  8 |  24 | 12
--------------------+----+----+-----+---
x .   .   .         |  2 | 96 |   6 |  6
--------------------+----+----+-----+---
x3o   .   .         |  3 |  3 | 192 |  2
--------------------+----+----+-----+---
x3o4/3o   .       & ♦  6 | 12 |   8 | 48


x3/2o4o3o4/3*b   (Type B)

.   . . .      | 24 ♦  8 |  24 |  6  6
---------------+----+----+-----+------
x   . . .      |  2 | 96 |   6 |  3  3
---------------+----+----+-----+------
x3/2o . .      |  3 |  3 | 192 |  1  1
---------------+----+----+-----+------
x3/2o4o .      ♦  6 | 12 |   8 | 24  *
x3/2o . o4/3*b ♦  6 | 12 |   8 |  * 24


x3/2o4o3/2o4*b   (Type B)

.   . .   .    | 24 ♦  8 |  24 |  6  6
---------------+----+----+-----+------
x   . .   .    |  2 | 96 |   6 |  3  3
---------------+----+----+-----+------
x3/2o .   .    |  3 |  3 | 192 |  1  1
---------------+----+----+-----+------
x3/2o4o   .    ♦  6 | 12 |   8 | 24  *
x3/2o .   o4*b ♦  6 | 12 |   8 |  * 24

or
.   . .   .       | 24 ♦  8 |  24 | 12
------------------+----+----+-----+---
x   . .   .       |  2 | 96 |   6 |  6
------------------+----+----+-----+---
x3/2o .   .       |  3 |  3 | 192 |  2
------------------+----+----+-----+---
x3/2o4o   .     & ♦  6 | 12 |   8 | 48


x3/2o4/3o3/2o4/3*b   (Type B)

.   .   .   .      | 24 ♦  8 |  24 |  6  6
-------------------+----+----+-----+------
x   .   .   .      |  2 | 96 |   6 |  3  3
-------------------+----+----+-----+------
x3/2o   .   .      |  3 |  3 | 192 |  1  1
-------------------+----+----+-----+------
x3/2o4/3o   .      ♦  6 | 12 |   8 | 24  *
x3/2o   .   o4/3*b ♦  6 | 12 |   8 |  * 24

or
.   .   .   .         | 24 ♦  8 |  24 | 12
----------------------+----+----+-----+---
x   .   .   .         |  2 | 96 |   6 |  6
----------------------+----+----+-----+---
x3/2o   .   .         |  3 |  3 | 192 |  2
----------------------+----+----+-----+---
x3/2o4/3o   .       & ♦  6 | 12 |   8 | 48

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