Acronym  biped 
Name  biprismatodecachoron 
Net 
© 
Circumradius  sqrt[(2a^{2}+ab+2b^{2})/5] 
Confer 

External links 
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 triapiculated 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/[4c^{2}/(ba)^{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 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 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 = ab 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
© 20042021  top of page 