Acronym | biped |
Name | biprismatodecachoron |
Net |
© |
Circumradius | sqrt[(2a2+ab+2b2)/5] |
Face vector | 40, 140, 160, 60 |
Confer |
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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 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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