Acronym | bipec |
Name | biprismatotetracontoctachoron |
Circumradius | sqrt[a2+ab sqrt(2)+b2] |
Face vector | 288, 1296, 1536, 528 |
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 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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