Acronym | retut (alt.: amtut) |
Name | rectified/ambified truncated tetrahedron |
© | |
Circumradius | sqrt(9/2) = 2.121320 |
Face vector | 18, 36, 20 |
Confer |
|
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 tut as a pre-image these intersection points might differ on its 2 edge types. Therefore tut 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 shorter one becomes unity. Then the larger edge will have size h=sqrt(3).
Incidence matrix according to Dynkin symbol
xox(do)-3-odd(od)-&#ht → height(1,2) = height(3,4) = sqrt(2/3) = 0.816497 height(2,3) = sqrt(8/3) = 1.632993 height(4,5) = 0 o..(..)-3-o..(..) | 3 * * * * | 2 2 0 0 0 0 0 | 1 2 1 0 0 0 0 .o.(..)-3-.o.(..) | * 3 * * * | 0 2 2 0 0 0 0 | 0 1 2 1 0 0 0 ..o(..)-3-..o(..) | * * 6 * * | 0 0 1 1 1 1 0 | 0 0 1 1 1 1 0 ...(o.)-3-...(o.) | * * * 3 * | 0 0 0 0 2 0 2 | 0 0 1 0 2 0 1 ...(.o)-3-...(.o) | * * * * 3 | 0 0 0 0 0 2 2 | 0 0 0 0 2 1 1 --------------------------+-----------+---------------+-------------- x..(..) ...(..) | 2 0 0 0 0 | 3 * * * * * * | 1 1 0 0 0 0 0 x oo.(..)-3-oo.(..)-&#h | 1 1 0 0 0 | * 6 * * * * * | 0 1 1 0 0 0 0 h .oo(..)-3-.oo(..)-&#h | 0 1 1 0 0 | * * 6 * * * * | 0 0 1 1 0 0 0 h ..x(..) ...(..) | 0 0 2 0 0 | * * * 3 * * * | 0 0 0 1 0 1 0 x ..o(o.)-3-..o(o.)-&#h | 0 0 1 1 0 | * * * * 6 * * | 0 0 1 0 1 0 0 h ..o(.o)-3-..o(.o)-&#x | 0 0 1 0 1 | * * * * * 6 * | 0 0 0 0 1 1 0 x ...(oo)-3-...(oo)-&#h | 0 0 0 1 1 | * * * * * * 6 | 0 0 0 0 1 0 1 h --------------------------+-----------+---------------+-------------- x..(..)-3-o..(..) | 3 0 0 0 0 | 3 0 0 0 0 0 0 | 1 * * * * * * x-{3} xo.(..) ...(..)-&#h | 2 1 0 0 0 | 1 2 0 0 0 0 0 | * 3 * * * * * xhh ...(..) odd(o.)-&#ht | 1 2 2 1 0 | 0 2 2 0 2 0 0 | * * 3 * * * * h-{6} .ox(..) ...(..)-&#h | 0 1 2 0 0 | 0 0 2 1 0 0 0 | * * * 3 * * * xhh ..o(oo)-3-..o(oo)-&#(h,x) | 0 0 1 1 1 | 0 0 0 0 1 1 1 | * * * * 6 * * xhh ..x(.o) ...(..)-&#x | 0 0 2 0 1 | 0 0 0 1 0 2 0 | * * * * * 3 * x-{3} ...(do)-3-...(od)-&#zh | 0 0 0 3 3 | 0 0 0 0 0 0 6 | * * * * * * 1 h-{6}
xo3od3do&#zh → height = 0 (tegum sum of x3o3d and d-oct) o.3o.3o. | 12 * | 2 2 | 1 2 1 .o3.o3.o | * 6 | 0 4 | 0 2 2 -------------+------+-------+------- x. .. .. | 2 0 | 12 * | 1 1 0 oo3oo3oo&#h | 1 1 | * 24 | 0 1 1 -------------+------+-------+------- x.3o. .. | 3 0 | 3 0 | 4 * * x-{3} xo .. ..&#h | 2 1 | 1 2 | * 12 * xhh .. od3do&#zh | 3 3 | 0 6 | * * 4 h-{6}
© 2004-2024 | top of page |