Acronym ...
Name oct+3{4} (?),
complex polyhedron x2-3-o2-4-o2
Circumradius 1/sqrt(2) = 0.707107
Coordinates (1/sqrt(2), 0, 0)   & all permutations, all changes of sign
General of army oct
Colonel of regiment oct
Confer oct+6{4}   2oct+6{4}   2oct+12{4}  

Looks like a compound of an octahedra (oct) plus 3 diametral squares.


Incidence matrix according to Dynkin symbol

x2-3-o2-4-o2

      .    .    .  | 6 |  4 | 4 2
-------------------+---+----+----
      x2   .    .  | 2 | 12 | 2 1
-------------------+---+----+----
      x2-3-o2   .  | 3 |  3 | 8 *
sefa: .    x2-4-o2 | 4 |  4 | * 3


o2-3-x2-3-o2

      .    .    .  | 6 |  4 | 2 2 2
-------------------+---+----+------
      .    x2   .  | 2 | 12 | 1 1 1
-------------------+---+----+------
      o2-3-x2   .  | 3 |  3 | 4 * *
sefa: x2   .    x2 | 4 |  4 | * 3 *
      .    x2-3-o2 | 3 |  3 | * * 4

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