Acronym bipec
Name biprismatotetracontoctachoron
Circumradius sqrt[a2+ab sqrt(2)+b2]
Confer
general polytopal classes:
isogonal  
External
links
polytopewiki

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 tetra-apiculated 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/[4c2/(b-a)2-1]) = arccos(1/[4(2-sqrt(2))-1]) = 41.882041° < 45° = 360°/8, i.e. the below provided seemingly huge number of 8 trapezoprisms around the c-edges 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 = |a-b| sqrt[2-sqrt(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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