Acronym | resrip (alt.: amsrip) |
Name | rectified/ambified srip |
Circumradius | sqrt(23/5) = 2.144761 |
Face vector | 90, 270, 230, 50 |
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 srip as a pre-image these intersection points might differ on its 2 edge types. Therefore srip 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 longer edge will have size q = sqrt(2).
The non-polar triangles {(t,T,T)} have vertex angles t = arccos(3/4) = 41.409622° resp. T = arccos[1/sqrt(8)] = 69.295189°.
All u = 2 edges, used in the below descriptions, only qualify as pseudo edges wrt. the full polychoron.
Incidence matrix according to Dynkin symbol
xo3ou3xx3uo&#zq → height = 0 o.3o.3o.3o. | 60 * | 2 2 2 0 | 1 2 1 2 1 2 0 | 1 1 2 1 .o3.o3.o3.o | * 30 | 0 0 4 2 | 0 0 0 2 2 4 1 | 0 1 2 2 ----------------+-------+--------------+----------------------+---------- x. .. .. .. | 2 0 | 60 * * * | 1 1 0 1 0 0 0 | 1 1 1 0 .. .. x. .. | 2 0 | * 60 * * | 0 1 1 0 0 1 0 | 1 0 1 1 oo3oo3oo3oo&#q | 1 1 | * * 120 * | 0 0 0 1 1 1 0 | 0 1 1 1 .. .. .x .. | 0 2 | * * * 30 | 0 0 0 0 0 2 1 | 0 0 1 2 ----------------+-------+--------------+----------------------+---------- x.3o. .. .. | 3 0 | 3 0 0 0 | 20 * * * * * * | 1 1 0 0 x. .. x. .. | 4 0 | 2 2 0 0 | * 30 * * * * * | 1 0 1 0 .. o.3x. .. | 3 0 | 0 3 0 0 | * * 20 * * * * | 1 0 0 1 xo .. .. ..&#q | 2 1 | 1 0 2 0 | * * * 60 * * * | 0 1 1 0 .. ou .. uo&#zq | 2 2 | 0 0 4 0 | * * * * 30 * * | 0 1 0 1 .. .. xx ..&#q | 2 2 | 0 1 2 1 | * * * * * 60 * | 0 0 1 1 .. .. .x3.o | 0 3 | 0 0 0 3 | * * * * * * 10 | 0 0 0 2 ----------------+-------+--------------+----------------------+---------- x.3o.3x. .. ♦ 12 0 | 12 12 0 0 | 4 6 4 0 0 0 0 | 5 * * * xo3ou .. uo&#zq ♦ 6 3 | 6 0 12 0 | 2 0 0 6 3 0 0 | * 10 * * xo .. xx ..&#q ♦ 4 2 | 2 2 4 1 | 0 1 0 2 0 2 0 | * * 30 * .. ou3xx3uo&#zq ♦ 12 12 | 0 12 24 12 | 0 0 4 0 6 12 4 | * * * 5
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