Acronym ...
Name icosa-expanded rhombic enneacontahedron
  
 ©
Vertex figure [r5], [r,h,3,h], [R2,H]
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Face vector 132, 240, 110

The rhombs {(r,R)2} have vertex angles r = arccos(1/3) = 70.528779° resp. R = arccos(-1/3) = 109.471221°. Esp. rr : RR = sqrt(2) = 1.414214.
The hexagons {(h,h,H)2} have vertex angles h = arccos(-sqrt[(3-sqrt(5))/6]) = 110.905157° resp. H = arccos[-sqrt(5)/3] = 138.189685°.

This polyhedron is just the Stott expansion of the rhombic enneacontahedron wrt. its icosahedral vertices.

All a, b, c, and d edges, provided in the below description, only qualify as pseudo edges wrt. the full polyhedron.


Incidence matrix according to Dynkin symbol

((abx3oco5ood))&#zx   → height = 0, 
                        a = 1+sqrt(20/3) = 3.581989,
                        b = HH = 1+(sqrt(5)-1)/sqrt(3) = 1.713644,
                        c = RR = 2/sqrt(3) = 1.154701,
                        d = hh = (1+sqrt(5))/sqrt(3) = 1.868345

  o..3o..5o..       | 12  *  * |  5   0  0 |  5  0  0  [r5]
  .o.3.o.5.o.       |  * 60  * |  1   2  0 |  2  1  0  [R2,H]
  ..o3..o5..o       |  *  * 60 |  0   2  2 |  1  2  1  [r,h,3,h]
--------------------+----------+-----------+---------
  oo.3oo.5oo.  &#x  |  1  1  0 | 60   *  * |  2  0  0
  .oo3.oo5.oo  &#x  |  0  1  1 |  * 120  * |  1  1  0
  ..x ... ...       |  0  0  2 |  *   * 60 |  0  1  1
--------------------+----------+-----------+---------
  ... oco ...  &#xt |  1  2  1 |  2   2  0 | 60  *  *  {(r,R)2}
((.bx ... .od))&#zx |  0  2  4 |  0   4  2 |  * 30  *  {(h,h,H)2}
  ..x3..o ...       |  0  0  3 |  0   0  3 |  *  * 20

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