Acronym ...
Name rox+720pip (?)
Circumradius sqrt[5+2 sqrt(5)] = 3.077684
General of army rox
Colonel of regiment rox
Confer
non-Grünbaumian master:
rox  
Grünbaumian relatives:
2rox   2rox+1440{5}+2400{3}   2rox+sophi  

This is an edge-faceting of (the Grünbaumian double cover of) the rectified hexacosachoron (rox). The 720 pentagonal prisms (pip) are the vertex figures of the rectified hexacosachoron, and their faces are facets of its former cells which thus get an inner structure.


Incidence matrix according to Dynkin symbol

o3β3o5o

both( . . . . ) | 720 |   10   20 |    5   10   20   10 |   5   2  10
----------------+-----+-----------+---------------------+------------
sefa( o3β . . ) |   2 | 3600    * |    1    0    2    0 |   2   0   1
sefa( . β3o . ) |   2 |    * 7200 |    0    1    1    1 |   1   1   1
----------------+-----+-----------+---------------------+------------
      o3β . .      3 |    3    0 | 1200    *    *    * |   2   0   0
      . β3o .      3 |    0    3 |    * 2400    *    * |   1   1   0
sefa( o3β3o . ) |   4 |    2    2 |    *    * 3600    * |   1   0   1
sefa( . β3o5o ) |   5 |    0    5 |    *    *    * 1440 |   0   1   1
----------------+-----+-----------+---------------------+------------
      o3β3o .      6 |   12   12 |    4    4    6    0 | 600   *   *
      . β3o5o     12 |    0   60 |    0   20    0   12 |   * 120   *
sefa( o3β3o5o )   10 |    5   10 |    0    0    5    2 |   *   * 720

starting figure: o3x3o5o

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