Acronym | pibhaki |
Name |
pentagonal-bipyramidal heptacosiicosachoron, rectified-hexacosachoron dual, surtegmated hecatonicosachoron |
© (partial display of cells around a common vertex only) | |
Dual | rox |
External links |
This polychoron can be obtained from the compound of a unit ex and a scaled dual hi, when choosing the edge center radius of ex and the pentagon center radius of hi to be equal. Then the convex hull therefrom results in this polychoron, and the edges of the former resp. the orthogonal pentagons of the latter will serve as diametrals of the cells of this hull polychoron.
All c edges, provided in the below description, only qualify as pseudo edges wrt. the full polychoron. In fact those are the tip-to-tip diametrals of the cells, which all are identical co oo5ox&#zy bipyramids.
Because o3m3o5o is derived by some secondary process only (rectification followed by dualisation), instead of a primary Wythoff construction, it is much more remarkable that it still allows for rectification (oq3oo3qo5oc&zx). This is because the truncational depth of the second vertex type (in the below incidence matrix) for a rectification scenario is easily settled at the second edge type (providing the mid points at those x-edges). But then the same truncational hyperplanes would define corresponding intersection points on the y-edges as well. And those points then could be matched in a rectificational sense by truncation hyperplanes of according depth wrt. the first vertex set.
Incidence matrix according to Dynkin symbol
o3m3o5o = co3oo3oo5ox&#zy → height = 0 c = (5+3 sqrt(5))/5 = 2.341641 (tip-to-tip diametrals) y = sqrt[(6+2 sqrt(5))/5] = 1.447214 (lacing edges) o.3o.3o.5o. | 120 * ♦ 20 0 | 30 | 12 .o3.o3.o5.o | * 600 ♦ 4 4 | 12 | 6 ----------------+---------+-----------+------+---- oo3oo3oo5oo&#y | 1 1 | 2400 * | 3 | 3 .. .. .. .x | 0 2 | * 1200 | 3 | 3 ----------------+---------+-----------+------+---- .. .. .. ox&#y | 1 2 | 2 1 | 3600 | 2 ----------------+---------+-----------+------+---- co .. oo5ox&#zy ♦ 2 5 | 10 5 | 10 | 720
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