Acronym biped
Name biprismatodecachoron
Net
 ©
Circumradius sqrt[(2a2+ab+2b2)/5]
Confer
general polytopal classes:
isogonal  
External
links
hedrondude   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 tri-apiculated trigonal 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/[12/5 - 1]) = 44.415309° < 60° = 360°/6, i.e. the below provided seemingly huge number of 6 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 triangle, might give some further restriction to the a:b ratio, which so far has not been evaluated.


Incidence matrix according to Dynkin symbol

ab3oo3oo3ba&#zc   → height = 0
                    a < b
                    c = |a-b| sqrt(3/5)

o.3o.3o.3o.     & | 40 |  3  3  1 |  3  6  6 |  1  3  6
------------------+----+----------+----------+---------
a. .. .. ..     & |  2 | 60  *  * |  2  2  1 |  1  2  2
.. .. .. b.     & |  2 |  * 60  * |  0  2  1 |  0  1  2
oo3oo3oo3oo&#c    |  2 |  *  * 20 |  0  0  6 |  0  0  6
------------------+----+----------+----------+---------
a.3o. .. ..     & |  3 |  3  0  0 | 40  *  * |  1  1  0
a. .. .. b.     & |  4 |  2  2  0 |  * 60  * |  0  1  1
ab .. .. ..&#c  & |  4 |  1  1  2 |  *  * 60 |  0  0  2
------------------+----+----------+----------+---------
a.3o.3o. ..     & |  4 |  6  0  0 |  4  0  0 | 10  *  *  tet
a.3o. .. b.     & |  6 |  6  3  0 |  2  3  0 |  * 20  *  trip
ab .. .. ba&#c    |  8 |  4  4  4 |  0  2  4 |  *  * 30  recta

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