o  
  c
o  

where:
o = x3o4o (oct)
c = o3o4x (cube)

If at the base ope both oct bases in turn would get diminished down to a diametral square, then the whole base would become a cube too. Using that in here then results in squiddaf (= {4}-prism || bidual {4}-prism).

Incidence matrix according to Dynkin symbol

ox ox3oo4xo&#x   → height = sqrt[(sqrt(2)-1)/2] = 0.455090
(cube || ope)

o. o.3o.4o.    | 8  * |  3  6 0  0 | 3  3  6 12  0  0 | 1  3  6  2  6  6 0 0 | 1  3 3 2 0
.o .o3.o4.o    | * 12 |  0  4 1  4 | 0  4  8  4  4  4 | 0  8  4  4  4  1 4 1 | 4  4 1 1 1
---------------+------+------------+------------------+----------------------+-----------
.. .. .. x.    | 2  0 | 12  * *  * | 2  0  0  4  0  0 | 1  0  2  0  2  4 0 0 | 0  1 2 2 0
oo oo3oo4oo&#x | 1  1 |  * 48 *  * | 0  1  2  2  0  0 | 0  2  2  1  2  1 0 0 | 1  2 1 1 0
.x .. .. ..    | 0  2 |  *  * 6  * | 0  4  0  0  4  0 | 0  8  4  0  0  0 4 0 | 4  4 1 0 1
.. .x .. ..    | 0  2 |  *  * * 24 | 0  0  2  0  1  2 | 0  2  0  2  1  0 2 1 | 2  1 0 1 1
---------------+------+------------+------------------+----------------------+-----------
.. .. o.4x.    | 4  0 |  4  0 0  0 | 6  *  *  *  *  * | 1  0  0  0  0  2 0 0 | 0  0 1 2 0
ox .. .. ..&#x | 1  2 |  0  2 1  0 | * 24  *  *  *  * | 0  2  2  0  0  0 0 0 | 1  2 1 0 0
.. ox .. ..&#x | 1  2 |  0  2 0  1 | *  * 48  *  *  * | 0  1  0  1  1  0 0 0 | 1  1 0 1 0
.. .. .. xo&#x | 2  1 |  1  2 0  0 | *  *  * 48  *  * | 0  0  1  0  1  1 0 0 | 0  1 1 1 0
.x .x .. ..    | 0  4 |  0  0 2  2 | *  *  *  * 12  * | 0  2  0  0  0  0 2 0 | 2  1 0 0 1
.. .x3.o ..    | 0  3 |  0  0 0  3 | *  *  *  *  * 16 | 0  0  0  1  0  0 1 1 | 1  0 0 1 1
---------------+------+------------+------------------+----------------------+-----------
.. o.3o.4x.    ♦ 8  0 | 12  0 0  0 | 6  0  0  0  0  0 | 1  *  *  *  *  * * * | 0  0 0 2 0
ox ox .. ..&#x ♦ 1  4 |  0  4 2  2 | 0  2  2  0  1  0 | * 24  *  *  *  * * * | 1  1 0 0 0
ox .. .. xo&#x ♦ 2  2 |  1  4 1  0 | 0  2  0  2  0  0 | *  * 24  *  *  * * * | 0  1 1 0 0
.. ox3oo ..&#x ♦ 1  3 |  0  3 0  3 | 0  0  3  0  0  1 | *  *  * 16  *  * * * | 1  0 0 1 0
.. ox .. xo&#x ♦ 2  2 |  1  4 0  1 | 0  0  2  2  0  0 | *  *  *  * 24  * * * | 0  1 0 1 0
.. .. oo4xo&#x ♦ 4  1 |  4  4 0  0 | 1  0  0  4  0  0 | *  *  *  *  * 12 * * | 0  0 1 1 0
.x .x3.o ..    ♦ 0  6 |  0  0 3  6 | 0  0  0  0  3  2 | *  *  *  *  *  * 8 * | 1  0 0 0 1
.. .x3.o4.o    ♦ 0  6 |  0  0 0 12 | 0  0  0  0  0  8 | *  *  *  *  *  * * 2 | 0  0 0 1 1 
---------------+------+------------+------------------+----------------------+-----------
ox ox3oo ..&#x ♦ 1  6 |  0  6 3  6 | 0  3  6  0  3  2 | 0  3  0  2  0  0 1 0 | 8  * * * *
ox ox .. xo&#x ♦ 2  4 |  1  8 2  2 | 0  4  4  4  1  0 | 0  2  2  0  2  0 0 0 | * 12 * * *
ox .. oo4xo&#x ♦ 4  2 |  4  8 1  0 | 1  4  0  8  0  0 | 0  0  4  0  0  2 0 0 | *  * 6 * *
.. ox3oo4xo&#x ♦ 8  6 | 12 24 0 12 | 6  0 24 24  0  8 | 1  0  0  8 12  6 0 1 | *  * * 2 *
.x .x3.o4.o    ♦ 0 12 |  0  0 6 24 | 0  0  0  0 12 16 | 0  0  0  0  0  0 8 2 | *  * * * 1