Acronym ...
Name 2did (?)
Circumradius 1
Vertex figure 2[(5/2,10/2)2] (type A) or
2[(10/4,5)2] (type B)
General of army id
Colonel of regiment did
Confer
non-Grünbaumian master:
did  

Looks like a compound of 2 dodecadodecahedra (did), and indeed vertices, edges, and either {5/2} (type A) or {5} (type B) all coincide by pairs.


Incidence matrix according to Dynkin symbol

x5/2x5/2o5/2*a (type A)

.   .   .      | 60 |  2  2 |  2  1  1
---------------+----+-------+---------
x   .   .      |  2 | 60  * |  1  1  0
.   x   .      |  2 |  * 60 |  1  0  1
---------------+----+-------+---------
x5/2x   .      | 10 |  5  5 | 12  *  *
x   .   o5/2*a |  5 |  5  0 |  * 12  *
.   x5/2o      |  5 |  0  5 |  *  * 12

x5/4x5o5*a (type B)

.   . .    | 60 |  2  2 |  2  1  1
-----------+----+-------+---------
x   . .    |  2 | 60  * |  1  1  0
.   x .    |  2 |  * 60 |  1  0  1
-----------+----+-------+---------
x5/4x .    | 10 |  5  5 | 12  *  *
x   . o5*a |  5 |  5  0 |  * 12  *
.   x5o    |  5 |  0  5 |  *  * 12

x5/3o5/3x5/2*a (type A)

.   .   .      | 60 |  2  2 |  1  2  1
---------------+----+-------+---------
x   .   .      |  2 | 60  * |  1  1  0
.   .   x      |  2 |  * 60 |  0  1  1
---------------+----+-------+---------
x5/3o   .      |  5 |  5  0 | 12  *  *
x   .   x5/2*a | 10 |  5  5 |  * 12  *
.   o5/3x      |  5 |  0  5 |  *  * 12

x5/4x5/4o5/4*a (type B)

.   .   .      | 60 |  2  2 |  2  1  1
---------------+----+-------+---------
x   .   .      |  2 | 60  * |  1  1  0
.   x   .      |  2 |  * 60 |  1  0  1
---------------+----+-------+---------
x5/4x   .      | 10 |  5  5 | 12  *  *
x   .   o5/4*a |  5 |  5  0 |  * 12  *
.   x5/4o      |  5 |  0  5 |  *  * 12

β5/2x5o (type B)

both( .   . . ) | 60 |  2  2 |  1  2  1
----------------+----+-------+---------
both( .   x . ) |  2 | 60  * |  1  1  0
sefa( β5/2x . ) |  2 |  * 60 |  0  1  1
----------------+----+-------+---------
both( .   x5o ) |  5 |  5  0 | 12  *  *
      β5/2x .    10 |  5  5 |  * 12  *
sefa( β5/2x5o ) |  5 |  0  5 |  *  * 12

starting figure: x5/2x5o

x5/2o5β (type A)

both( .   . . ) | 60 |  2  2 |  1  1  2
----------------+----+-------+---------
both( x   . . ) |  2 | 60  * |  1  0  1
sefa( .   o5β ) |  2 |  * 60 |  0  1  1
----------------+----+-------+---------
both( x5/2o . ) |  5 |  5  0 | 12  *  *
      .   o5β     5 |  0  5 |  * 12  *
sefa( x5/2o5β ) | 10 |  5  5 |  *  * 12

starting figure: x5/2o5x

o5/2x5β (type A)

both( .   . . ) | 60 |  2  2 |  1  2  1
----------------+----+-------+---------
both( .   x . ) |  2 | 60  * |  1  1  0
sefa( .   x5β ) |  2 |  * 60 |  0  1  1
----------------+----+-------+---------
both( o5/2x . ) |  5 |  5  0 | 12  *  *
      .   x5β    10 |  5  5 |  * 12  *
sefa( o5/2x5β ) |  5 |  0  5 |  *  * 12

starting figure: o5/2x5x

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