Acronym ...
Name 3pen (?)
Circumradius sqrt(2/5) = 0.632456
General of army pen
Colonel of regiment pen
Confer
non-Grünbaumian master:
pen  
Grünbaumian relatives:
2pen (?)   4pen+160{3} (?)  

Looks like a compound of 3 pentachora (pen) with vertices identified, edges and faces coincide by 3, cells by pairs. One of the coincident cells each is a Grünbaumian double cover of the tetrahedron (2tet (?)) itself.


Incidence matrix according to Dynkin symbol

β3o3o3o

both( . . . . ) | 5  12 |  6 12 | 4 4
----------------+---+----+-------+----
sefa( β3o . . ) | 2 | 30 |  1  2 | 2 1
----------------+---+----+-------+----
      β3o . .    3 |  3 | 10  * | 2 0
sefa( β3o3o . ) | 3 |  3 |  * 20 | 1 1
----------------+---+----+-------+----
      β3o3o .    4 | 12 |  4  4 | 5 *
sefa( β3o3o3o )  4 |  6 |  0  4 | * 5

starting figure: x3o3o3o

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