This polyhedron is isogonal only. It reflects the mere alternated faceting of the above depicted snub derivation wrt. a triangle-alternation with starting figure tut. However, it could be resized to all unit-sized edges, then resulting in the Grünbaumian 2oct (type A).

Incidence matrix according to Dynkin symbol

β3x3o

both( . . . ) | 12 |  2  2 | 2 1 1
--------------+----+-------+------
both( . x . ) |  2 | 12  * | 1 1 0  x
sefa( β3x . ) |  2 |  * 12 | 1 0 1  u
--------------+----+-------+------
      β3x .   ♦  6 |  3  3 | 4 * *
both( . x3o ) |  3 |  3  0 | * 4 *
sefa( β3x3o ) |  3 |  0  3 | * * 4

starting figure: x3x3o

o3/2x3β

both( .   . . ) | 12 |  2  2 | 1 2 1
----------------+----+-------+------
both( .   x . ) |  2 | 12  * | 1 1 0  x
sefa( .   x3β ) |  2 |  * 12 | 0 1 1  u
----------------+----+-------+------
both( o3/2x . ) |  3 |  3  0 | 4 * *
      .   x3β   ♦  6 |  3  3 | * 4 *
sefa( o3/2x3β ) |  3 |  0  3 | * * 4

starting figure: o3/2x3x

x3/2u3o3*a

.   . .    | 12 |  2  2 | 2 1 1
-----------+----+-------+------
x   . .    |  2 | 12  * | 1 1 0  x
.   u .    |  2 |  * 12 | 1 0 1  u
-----------+----+-------+------
x3/2u .    |  6 |  3  3 | 4 * *
x   . o3*a |  3 |  3  0 | * 4 *
.   u3o    |  3 |  0  3 | * * 4

x3/2u3/2o3/2*a

.   .   .      | 12 |  2  2 | 2 1 1
---------------+----+-------+------
x   .   .      |  2 | 12  * | 1 1 0  x
.   u   .      |  2 |  * 12 | 1 0 1  u
---------------+----+-------+------
x3/2u   .      |  6 |  3  3 | 4 * *
x   .   o3/2*a |  3 |  3  0 | * 4 *
.   u3/2o      |  3 |  0  3 | * * 4