Acronym  bipec 
Name  biprismatotetracontoctachoron 
Circumradius  sqrt[a^{2}+ab sqrt(2)+b^{2}] 
Confer 

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This isogonal polychoron cannot be made uniform, i.e. having all 3 edge types at the same size.
The incidence matrix below shows that the vertex figure is a tetraapiculated square pyramid.
Note that the below provided value of c (obtained from the zero height requirement of the tegum sum), when inserted into the formula of the dihedral angle of the lacing edge of the recta results in arccos(1/[4c^{2}/(ba)^{2}1]) = arccos(1/[4(2sqrt(2))1]) = 41.882041° < 45° = 360°/8, i.e. the below provided seemingly huge number of 8 trapezoprisms around the cedges indeed is valid here. Note moreover that the calculated value does no longer depend on the chosen ratio of a:b !
Sure, asking that the lacing edges of the pyramid are outside to the burried pseudo edges of the medial layer square, might give some further restriction to the a:b ratio, which so far has not been evaluated.
Incidence matrix according to Dynkin symbol
ab3oo4oo3ba&#zc → height = 0 a < b c = ab sqrt[2sqrt(2)] o.3o.4o.3o. &  288  4 4 1  4 8 8  1 4 8 ++++ a. .. .. .. &  2  576 * *  2 2 1  1 2 2 .. .. .. b. &  2  * 576 *  0 2 1  0 1 2 oo3oo4oo3oo&#c  2  * * 144  0 0 8  0 0 8 ++++ a.3o. .. .. &  3  3 0 0  384 * *  1 1 0 a. .. .. b. &  4  2 2 0  * 576 *  0 1 1 ab .. .. ..&#c &  4  1 1 2  * * 576  0 0 2 ++++ a.3o.4o. .. &  6  12 0 0  8 0 0  48 * * oct a.3o. .. b. &  6  6 3 0  2 3 0  * 192 * trip ab .. .. ba&#c  8  4 4 4  0 2 4  * * 288 recta
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