Acronym | rexhi (alt.: amxhi) |
Name | rectified/ambified hexacosihecatonicosachoron |
Circumradius | sqrt[117+50 sqrt(5)] = 15.126249 |
Face vector | 7200, 21600, 18720, 4320 |
Confer |
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Rectification wrt. a non-regular polytope is meant to be the singular instance of truncations on all vertices at such a depth that the hyperplane intersections on the former edges will coincide (provided such a choice exists). Within the specific case of xhi as a pre-image these intersection points might differ on its 2 edge types. Therefore xhi cannot be rectified (within this stronger sense). Nonetheless the Conway operator of ambification (chosing the former edge centers generally) clearly is applicable. This would result in 2 different edge sizes in the outcome polychoron. That one here is scaled such so that the smaller one becomes unity. Then the medium edge will have size f = (1+sqrt(5))/2 and the longer one has size h = sqrt(3).
All d = 3 edges, used in the below descriptions, only qualify as pseudo edges wrt. the full polychoron.
Incidence matrix according to Dynkin symbol
xo3od3do5of&#zh (h-laced tegum sum of (x,d)-srix and (d,f)-srahi) o.3o.3o.5o. | 3600 * | 2 4 0 | 1 4 2 2 0 | 2 2 1 .o3.o3.o5.o | * 3600 | 0 4 2 | 0 2 2 4 1 | 1 2 2 ----------------+-----------+-----------------+-------------------------+------------- x. .. .. .. | 2 0 | 3600 * * | 1 2 0 0 0 | 2 1 0 x oo3oo3oo5oo&#h | 1 1 | * 14400 * | 0 1 1 1 0 | 1 1 1 h .. .. .. .f | 0 2 | * * 3600 | 0 0 0 2 1 | 0 1 2 f ----------------+-----------+-----------------+-------------------------+------------- x.3o. .. .. | 3 0 | 3 0 0 | 1200 * * * * | 2 0 0 x-{3} xo .. .. ..&#h | 2 1 | 1 2 0 | * 7200 * * * | 1 1 0 {(xhh)} .. od3do ..&#zh | 3 3 | 0 6 0 | * * 2400 * * | 1 0 1 h-{6} .. .. .. of&#h | 1 2 | 0 2 1 | * * * 7200 * | 0 1 1 {(fhh)} .. .. .o5.f | 0 5 | 0 0 5 | * * * * 720 | 0 0 2 f-{5} ----------------+-----------+-----------------+-------------------------+------------- xo3od3do ..&#zh | 12 6 | 12 24 0 | 4 12 4 0 0 | 600 * * retut xo .. .. of&#h | 2 2 | 1 4 1 | 0 2 0 2 0 | * 3600 * 2-ap variant .. od3do5of&#zh | 30 60 | 0 120 60 | 0 0 20 60 12 | * * 120 reti
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