Acronym ...
Name 2oh (?)
Circumradius 1
Coordinates
    1. (1, 0, 0, 0)                & all permutations, all changes of sign
      (vertex inscribed 1/q-hex)
    2. (1/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign
      (vertex inscribed tes)
  • or just   (1/sqrt(2), 1/sqrt(2), 0, 0)   & all permutations, all changes of sign
    (in dual ico positioning)
General of army ico
Colonel of regiment ico
Confer
non-Grünbaumian master:
oh  

Looks like a coincidentic compound of 2 octihemihexadecachoron (oh). In fact, all elements coincide by pairs.


Incidence matrix according to Dynkin symbol

o4o3x3x3/2*b

. . . .      | 48 |  4  4 |  4  4  4 | 1 1  4
-------------+----+-------+----------+-------
. . x .      |  2 | 96  * |  2  0  1 | 1 0  2
. . . x      |  2 |  * 96 |  0  2  1 | 0 1  2
-------------+----+-------+----------+-------
. o3x .      |  3 |  3  0 | 64  *  * | 1 0  1
. o . x3/2*b |  3 |  0  3 |  * 64  * | 0 1  1
. . x3x      |  6 |  3  3 |  *  * 32 | 0 0  2
-------------+----+-------+----------+-------
o4o3x .        6 | 12  0 |  8  0  0 | 8 *  *
o4o . x3/2*b   6 |  0 12 |  0  8  0 | * 8  *
. o3x3x3/2*b  12 | 12 12 |  4  4  4 | * * 16

o4/3o3x3x3/2*b

.   . . .      | 48 |  4  4 |  4  4  4 | 1 1  4
---------------+----+-------+----------+-------
.   . x .      |  2 | 96  * |  2  0  1 | 1 0  2
.   . . x      |  2 |  * 96 |  0  2  1 | 0 1  2
---------------+----+-------+----------+-------
.   o3x .      |  3 |  3  0 | 64  *  * | 1 0  1
.   o . x3/2*b |  3 |  0  3 |  * 64  * | 0 1  1
.   . x3x      |  6 |  3  3 |  *  * 32 | 0 0  2
---------------+----+-------+----------+-------
o4/3o3x .        6 | 12  0 |  8  0  0 | 8 *  *
o4/3o . x3/2*b   6 |  0 12 |  0  8  0 | * 8  *
.   o3x3x3/2*b  12 | 12 12 |  4  4  4 | * * 16

x3o3/2x3o3/2*a3*c

. .   . .         | 48 |  4  4 |  2  4  2  2  2 | 2 1 2 1
------------------+----+-------+----------------+--------
x .   . .         |  2 | 96  * |  1  1  1  0  0 | 1 1 1 0
. .   x .         |  2 |  * 96 |  0  1  0  1  1 | 1 0 1 1
------------------+----+-------+----------------+--------
x3o   . .         |  3 |  3  0 | 32  *  *  *  * | 1 1 0 0
x .   x .   *a3*c |  6 |  3  3 |  * 32  *  *  * | 1 0 1 0
x .   . o3/2*a    |  3 |  3  0 |  *  * 32  *  * | 0 1 1 0
. o3/2x .         |  3 |  0  3 |  *  *  * 32  * | 1 0 0 1
. .   x3o         |  3 |  0  3 |  *  *  *  * 32 | 0 0 1 1
------------------+----+-------+----------------+--------
x3o3/2x .   *a3*c  12 | 12 12 |  4  4  0  4  0 | 8 * * *
x3o   . o3/2*a      6 | 12  0 |  4  0  4  0  0 | * 8 * *
x .   x3o3/2*a3*c  12 | 12 12 |  0  4  4  0  4 | * * 8 *
. o3/2x3o           6 |  0 12 |  0  0  0  4  4 | * * * 8
or
. .   . .          & | 48 |   8 |  4  4  4 |  4  2
---------------------+----+-----+----------+------
x .   . .          & |  2 | 192 |  1  1  1 |  2  1
---------------------+----+-----+----------+------
x3o   . .          & |  3 |   3 | 64  *  * |  1  1
x .   x .   *a3*c    |  6 |   6 |  * 32  * |  2  0
x .   . o3/2*a     & |  3 |   3 |  *  * 64 |  1  1
---------------------+----+-----+----------+------
x3o3/2x .   *a3*c  &  12 |  24 |  4  4  4 | 16  *
x3o   . o3/2*a     &   6 |  12 |  4  0  4 |  * 16

x3o3/2x3/2o3*a3*c

. .   .   .       | 48 |  4  4 |  2  4  2  2  2 | 2 1 2 1
------------------+----+-------+----------------+--------
x .   .   .       |  2 | 96  * |  1  1  1  0  0 | 1 1 1 0
. .   x   .       |  2 |  * 96 |  0  1  0  1  1 | 1 0 1 1
------------------+----+-------+----------------+--------
x3o   .   .       |  3 |  3  0 | 32  *  *  *  * | 1 1 0 0
x .   x   . *a3*c |  6 |  3  3 |  * 32  *  *  * | 1 0 1 0
x .   .   o3*a    |  3 |  3  0 |  *  * 32  *  * | 0 1 1 0
. o3/2x   .       |  3 |  0  3 |  *  *  * 32  * | 1 0 0 1
. .   x3/2o       |  3 |  0  3 |  *  *  *  * 32 | 0 0 1 1
------------------+----+-------+----------------+--------
x3o3/2x   . *a3*c  12 | 12 12 |  4  4  0  4  0 | 8 * * *
x3o   .   o3*a      6 | 12  0 |  4  0  4  0  0 | * 8 * *
x .   x3/2o3*a3*c  12 | 12 12 |  0  4  4  0  4 | * * 8 *
. o3/2x3/2o         6 |  0 12 |  0  0  0  4  4 | * * * 8
or
. .   .   .        & | 48 |  4  4 |  4  4  4 |  4 1 1
---------------------+----+-------+----------+-------
x .   .   .          |  2 | 96  * |  2  1  0 |  2 1 0
. .   x   .          |  2 |  * 96 |  0  1  2 |  2 0 1
---------------------+----+-------+----------+-------
x3o   .   .        & |  3 |  3  0 | 64  *  * |  1 1 0
x .   x   . *a3*c    |  6 |  3  3 |  * 32  * |  2 0 0
. o3/2x   .        & |  3 |  0  3 |  *  * 64 |  1 0 1
---------------------+----+-------+----------+-------
x3o3/2x   . *a3*c  &  12 | 12 12 |  4  4  4 | 16 * *
x3o   .   o3*a         6 | 12  0 |  8  0  0 |  * 8 *
. o3/2x3/2o            6 |  0 12 |  0  0  8 |  * * 8

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