Acronym ...
Name x3w4o,
variation of truncated octahedron,
hull of rah,
hull of snu
Circumradius sqrt[(9+6 sqrt(2))/2] = 2.956796
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Confer toe   a3b3c   x3x3u   a3b4c   x3f4o   x3u4o   u3x4o   rah   snu  

Incidence matrix according to Dynkin symbol

x3w4o

. . . | 24 |  1  2 | 2 1
------+----+-------+----
x . . |  2 | 12  * | 2 0
. w . |  2 |  * 24 | 1 1
------+----+-------+----
x3w . |  6 |  3  3 | 8 *
. w4o |  4 |  0  4 | * 6

x3w4/3o

. .   . | 24 |  1  2 | 2 1
--------+----+-------+----
x .   . |  2 | 12  * | 2 0
. w   . |  2 |  * 24 | 1 1
--------+----+-------+----
x3w   . |  6 |  3  3 | 8 *
. w4/3o |  4 |  0  4 | * 6

w3x3w

. . . | 24 |  1  1  1 | 1 1 1
------+----+----------+------
w . . |  2 | 12  *  * | 1 1 0
. x . |  2 |  * 12  * | 1 0 1
. . w |  2 |  *  * 12 | 0 1 1
------+----+----------+------
w3x . |  6 |  3  3  0 | 4 * *
w . w |  4 |  2  0  2 | * 6 *
. x3w |  6 |  0  3  3 | * * 4

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