Acronym ...
Name hex+8oct (?)
Circumradius 1/sqrt(2) = 0.707107
General of army hex
Colonel of regiment hex
Confer hex   2hex+8oct  

Looks like a compound of an hexadecachoron (hex) with 8 pairwise coincident diametral octahedra (oct).


Incidence matrix according to Dynkin symbol

x3o3o4o4/3*b

. . . .      | 8   6 | 24 |  8 6
-------------+---+----+----+-----
x . . .      | 2 | 24 |  8 |  4 4
-------------+---+----+----+-----
x3o . .      | 3 |  3 | 64 |  1 1
-------------+---+----+----+-----
x3o3o .       4 |  6 |  4 | 16 *
x3o . o4/3*b  6 | 12 |  8 |  * 8

x3o3o4/3o4*b

. . .   .    | 8   6 | 24 |  8 6
-------------+---+----+----+-----
x . .   .    | 2 | 24 |  8 |  4 4
-------------+---+----+----+-----
x3o .   .    | 3 |  3 | 64 |  1 1
-------------+---+----+----+-----
x3o3o   .     4 |  6 |  4 | 16 *
x3o .   o4*b  6 | 12 |  8 |  * 8

x3o3/2o4o4*b

. .   . .    | 8   6 | 24 |  8 6
-------------+---+----+----+-----
x .   . .    | 2 | 24 |  8 |  4 4
-------------+---+----+----+-----
x3o   . .    | 3 |  3 | 64 |  1 1
-------------+---+----+----+-----
x3o3/2o .     4 |  6 |  4 | 16 *
x3o   . o4*b  6 | 12 |  8 |  * 8

x3o3/2o4/3o4/3*b

. .   .   .      | 8   6 | 24 |  8 6
-----------------+---+----+----+-----
x .   .   .      | 2 | 24 |  8 |  4 4
-----------------+---+----+----+-----
x3o   .   .      | 3 |  3 | 64 |  1 1
-----------------+---+----+----+-----
x3o3/2o   .       4 |  6 |  4 | 16 *
x3o   .   o4/3*b  6 | 12 |  8 |  * 8

x3/2o3o4o4/3*b

.   . . .      | 8   6 | 24 |  8 6
---------------+---+----+----+-----
x   . . .      | 2 | 24 |  8 |  4 4
---------------+---+----+----+-----
x3/2o . .      | 3 |  3 | 64 |  1 1
---------------+---+----+----+-----
x3/2o3o .       4 |  6 |  4 | 16 *
x3/2o . o4/3*b  6 | 12 |  8 |  * 8

x3/2o3o4/3o4*b

.   . .   .    | 8   6 | 24 |  8 6
---------------+---+----+----+-----
x   . .   .    | 2 | 24 |  8 |  4 4
---------------+---+----+----+-----
x3/2o .   .    | 3 |  3 | 64 |  1 1
---------------+---+----+----+-----
x3/2o3o   .     4 |  6 |  4 | 16 *
x3/2o .   o4*b  6 | 12 |  8 |  * 8

x3/2o3/2o4o4*b

.   .   . .    | 8   6 | 24 |  8 6
---------------+---+----+----+-----
x   .   . .    | 2 | 24 |  8 |  4 4
---------------+---+----+----+-----
x3/2o   . .    | 3 |  3 | 64 |  1 1
---------------+---+----+----+-----
x3/2o3/2o .     4 |  6 |  4 | 16 *
x3/2o   . o4*b  6 | 12 |  8 |  * 8

x3/2o3/2o4/3o4/3*b

.   .   .   .      | 8   6 | 24 |  8 6
-------------------+---+----+----+-----
x   .   .   .      | 2 | 24 |  8 |  4 4
-------------------+---+----+----+-----
x3/2o   .   .      | 3 |  3 | 64 |  1 1
-------------------+---+----+----+-----
x3/2o3/2o   .       4 |  6 |  4 | 16 *
x3/2o   .   o4/3*b  6 | 12 |  8 |  * 8

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