Acronym ...
Name rectified m m3o,
o2o3o symmetric co relative
Circumradius sqrt(2/3) = 0.816497
Confer
other axial symmetries:
co   oqo5coc&#xt  
variations:
obo3coc&#xt (c = b/2 = 1/sqrt(3))   obo3coc&#xt (c = b/2 = sqrt(2/3))   obo3coc&#xt (c = b/2 = sqrt[(5+sqrt(5))/10])  

Rectification wrt. a non-regular polytope is meant to be the singular instance of truncations on all vertices at such a depth that the hyperplane intersections on the former edges will coincide (provided such a choice exists).

The 6 non-polar triangles {(t,T,T)} have vertex angles t = arccos(3/4) = 41.409622° resp. T = arccos[1/sqrt(8)] = 69.295189°.

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


Incidence matrix according to Dynkin symbol

oqo3coc&#xt   → both heights = c = q/2 = 1/sqrt(2) = 0.707107

o..3o..     | 3 * * | 2 2 0 0 | 1 2 1 0 0
.o.3.o.     | * 3 * | 0 2 2 0 | 0 1 2 1 0
..o3..o     | * * 3 | 0 0 2 2 | 0 0 1 2 1
------------+-------+---------+----------
... c..     | 2 0 0 | 3 * * * | 1 1 0 0 0  c
oo.3oo.&#x  | 1 1 0 | * 6 * * | 0 1 1 0 0  x
.oo3.oo&#x  | 0 1 1 | * * 6 * | 0 0 1 1 0  x
... ..c     | 0 0 2 | * * * 3 | 0 0 0 1 1  c
------------+-------+---------+----------
o..3c..     | 3 0 0 | 3 0 0 0 | 1 * * * *  c-{3}
... co.&#x  | 2 1 0 | 1 2 0 0 | * 3 * * *  {(t,T,T)}
oqo ...&#xt | 1 2 1 | 0 2 2 0 | * * 3 * *  {4}
... .oc&#x  | 0 1 2 | 0 0 2 1 | * * * 3 *  {(t,T,T)}
..o3..c     | 0 0 3 | 0 0 0 3 | * * * * 1  c-{3}
or
o..3o..     & | 6 * | 2  2 | 1 2 1
.o.3.o.       | * 3 | 0  4 | 0 2 2
--------------+-----+------+------
... c..     & | 2 0 | 6  * | 1 1 0  c
oo.3oo.&#x  & | 1 1 | * 12 | 0 1 1  x
--------------+-----+------+------
o..3c..     & | 3 0 | 3  0 | 2 * *  c-{3}
... co.&#x  & | 2 1 | 1  2 | * 6 *  {(t,T,T)}
oqo ...&#xt   | 2 2 | 0  4 | * * 3  {4}

oq qo3oc&#zx   → height = 0, c = q/2 = 1/sqrt(2) = 0.707107
(tegum sum of q-{3} and gyrated (q,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  x
.. .. .c     | 0 2 |  * 6 | 0 1 1  c
-------------+-----+------+------
oq qo ..&#zx | 2 2 |  4 0 | 3 * *  {4}
.. .. oc&#x  | 1 2 |  2 1 | * 6 *  {(t,T,T)}
.. .o3.c     | 0 3 |  0 3 | * * 2  c-{3}

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