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

Incidence matrix according to Dynkin symbol

obo3coc&#xt   → both heights = sqrt[(5-sqrt(5))/10] = 0.525731
                b = 2 sqrt[(5+sqrt(5))/10] = 1.701302 (occurs just as long diagonal of rhomb of rhote)
                c = sqrt[(5+sqrt(5))/10] = 0.850651 (occurs as edge size)

o..3o..     & | 6 * | 2  2 | 1 2 1
.o.3.o.       | * 3 | 0  4 | 0 2 2
--------------+-----+------+------
... c..     & | 2 0 | 6  * | 1 1 0
oo.3oo.&#x  & | 1 1 | * 12 | 0 1 1
--------------+-----+------+------
o..3c..     & | 3 0 | 3  0 | 2 * *
... co.&#x  & | 2 1 | 1  2 | * 6 *
obo ...&#xt   | 2 2 | 0  4 | * * 3  {(r,R)2}

oa bo3oc&#zx   → height = 0
                 a = RR = 2 sqrt[(5-sqrt(5))/10] = 1.051462 (occurs just as small diagonal of rhomb of rhote)
                 b = rr = 2 sqrt[(5+sqrt(5))/10] = 1.701302 (occurs just as long diagonal of rhomb of rhote)
                 c = sqrt[(5+sqrt(5))/10] = 0.850651 (occurs as edge size)
(tegum sum of b-{3} and gyrated (a,c)-trip)

o. o.3o.     | 3 * |  4 0 | 2 2 0
.o .o3.o     | * 6 |  2 2 | 1 2 1
-------------+-----+------+------
oo oo3oo&#x  | 1 1 | 12 * | 1 1 0
.. .. .c     | 0 2 |  * 6 | 0 1 1
-------------+-----+------+------
oa bo ..&#zx | 2 2 |  4 0 | 3 * *  {(r,R)2}
.. .. oc&#x  | 1 2 |  2 1 | * 6 *
.. .o3.c     | 0 3 |  0 3 | * * 2