Acronym | retrip (alt.: amtrip) |
Name |
rectified/ambified trip, kernel of trip and m m3o, o2o3o symmetric co relative |
© | |
Circumradius | sqrt(2/3) = 0.816497 |
Face vector | 9, 18, 11 |
Confer |
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External links |
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 trip as a pre-image these intersection points might differ on its 2 edge types. Therefore trip 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 polyhedron. That one here is scaled such so that the larger one becomes unity. Then the shorter edge will have size c = q/2 = 1/sqrt(2).
The 6 non-polar triangles {(t,T,T)} have vertex angles t = arccos(3/4) = 41.409622° resp. T = arccos[1/sqrt(8)] = 69.295189°.
All q = sqrt(2) edges, used in the below descriptions, only qualify as pseudo edges wrt. the full polyhedron.
Note that the below description also could be scaled by q into a further convenient form ouo3xox&#qt = ou uo3ox&#zq, but then the circumradius and given heights too had to be rescaled accordingly for sure. Thereby the u-edges then would qualify as those pseudo edges.
Incidence matrix according to Dynkin symbol
oqo3coc&#xt → both heights = c = q/2 = 1/sqrt(2) = 0.707107 o..3o.. | 3 * * | 2 2 0 0 | 1 2 1 0 0 .o.3.o. | * 3 * | 0 2 2 0 | 0 1 2 1 0 ..o3..o | * * 3 | 0 0 2 2 | 0 0 1 2 1 ------------+-------+---------+---------- ... c.. | 2 0 0 | 3 * * * | 1 1 0 0 0 c oo.3oo.&#x | 1 1 0 | * 6 * * | 0 1 1 0 0 x .oo3.oo&#x | 0 1 1 | * * 6 * | 0 0 1 1 0 x ... ..c | 0 0 2 | * * * 3 | 0 0 0 1 1 c ------------+-------+---------+---------- o..3c.. | 3 0 0 | 3 0 0 0 | 1 * * * * c-{3} ... co.&#x | 2 1 0 | 1 2 0 0 | * 3 * * * {(t,T,T)} oqo ...&#xt | 1 2 1 | 0 2 2 0 | * * 3 * * {4} ... .oc&#x | 0 1 2 | 0 0 2 1 | * * * 3 * {(t,T,T)} ..o3..c | 0 0 3 | 0 0 0 3 | * * * * 1 c-{3}
or o..3o.. & | 6 * | 2 2 | 1 2 1 .o.3.o. | * 3 | 0 4 | 0 2 2 --------------+-----+------+------ ... c.. & | 2 0 | 6 * | 1 1 0 c oo.3oo.&#x & | 1 1 | * 12 | 0 1 1 x --------------+-----+------+------ o..3c.. & | 3 0 | 3 0 | 2 * * c-{3} ... co.&#x & | 2 1 | 1 2 | * 6 * {(t,T,T)} oqo ...&#xt | 2 2 | 0 4 | * * 3 {4}
oq qo3oc&#zx → height = 0, c = q/2 = 1/sqrt(2) = 0.707107 (tegum sum of q-{3} and gyrated (q,c)-trip) o. o.3o. | 3 * | 4 0 | 2 2 0 .o .o3.o | * 6 | 2 2 | 1 2 1 -------------+-----+------+------ oo oo3oo&#x | 1 1 | 12 * | 1 1 0 x .. .. .c | 0 2 | * 6 | 0 1 1 c -------------+-----+------+------ oq qo ..&#zx | 2 2 | 4 0 | 3 * * {4} .. .. oc&#x | 1 2 | 2 1 | * 6 * {(t,T,T)} .. .o3.c | 0 3 | 0 3 | * * 2 c-{3}
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