Acronym ...
Name truncated pedpy variant,
o2o5o symmetric co relative
Circumradius sqrt[1+1/sqrt(5)] = 1.203002
Confer
other axial symmetries:
oqo3coc&#xt   co  

All q = sqrt(2) edges, provided in the below description, only qualify as pseudo edges wrt. the full polyhedron.


Incidence matrix according to Dynkin symbol

oqo5coc&#xt   → both heights = 1/sqrt(2) = 0.707107, c = fq/2 = (1+sqrt(5))/sqrt(8) = 1.144123

o..5o..     & | 10 * |  2  2 | 1  2 1
.o.5.o.       |  * 5 |  0  4 | 0  2 2
--------------+------+-------+-------
... c..     & |  2 0 | 10  * | 1  1 0
oo.5oo.&#x  & |  1 1 |  * 20 | 0  1 1
--------------+------+-------+-------
o..5c..     & |  5 0 |  5  0 | 2  * *
... co.&#x  & |  2 1 |  1  2 | * 10 *
oqo ...&#xt   |  2 2 |  0  4 | *  * 5

oq qo5oc&#zx   → height = 0, c = fq/2 = (1+sqrt(5))/sqrt(8) = 1.144123
(tegum sum of q-{5} and gyrated (q,c)-pip)

o. o.5o.     | 5  * |  4  0 | 2  2 0
.o .o5.o     | * 10 |  2  2 | 1  2 1
-------------+------+-------+-------
oo oo5oo&#x  | 1  1 | 20  * | 1  1 0
.. .. .c     | 0  2 |  * 10 | 0  1 1
-------------+------+-------+-------
oq qo ..&#zx | 2  2 |  4  0 | 5  * *
.. .. oc&#x  | 1  2 |  2  1 | * 10 *
.. .o5.c     | 0  5 |  0  5 | *  * 2

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