Acronym ...
Name rhombical octa-augmented truncated-octehedral variant
  
 ©
Vertex figure [3,4,3,R], [(3,r)3]
Coordinates
  1. (sqrt(8)/3, sqrt(8)/3, sqrt(8)/3)     all changes of sign
    (vertex inscribed cube)
  2. (5 sqrt(2)/6, 1/sqrt(2), 0)             all permutations, all changes of sign
    (vertex inscribed truncated-octehedral variant)
Face vector 32, 72, 42
Confer expanded 8-augmented toe variant  

The short diagonal RR of the rhombs ((r,R)2) is 2/3 edge units, the long one rr then 4 sqrt(2)/3 edge units.
Their acute angle is r = arccos(7/9) = 38.942441°, the obtuse angle thus is R = arccos(-7/9) = 141.057559°.


Incidence matrix

24 * |  2  2 | 1  2  1  [3,4,3,R]
 * 8 |  0  6 | 0  3  3  [(3,r)3]
-----+-------+--------
 2 0 | 24  * | 1  1  0
 1 1 |  * 48 | 0  1  1
-----+-------+--------
 4 0 |  4  0 | 6  *  *  {4}
 2 1 |  1  2 | * 24  *  {3}
 2 2 |  0  4 | *  * 12  ((r,R)2)

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