Acronym | retic (alt.: amtic) |
Name | rectified/ambified truncated cube |
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Circumradius | 2+sqrt(2) = 3.414214 |
Face vector | 36, 72, 38 |
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 tic as a pre-image these intersection points might differ on its 2 edge types. Therefore tic 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 k = x(8) = sqrt[2+sqrt(2)] = 1.847759.
Incidence matrix according to Dynkin symbol
xo3oK4Ko&#zk → height = 0 K = kk = 2+sqrt(2) = 3.414214 (pseudo) k = x(8) = sqrt[2+sqrt(2)] = 1.847759 (tegum sum of (x,K)-sirco and K-co) o.3o.4o. | 24 * | 2 2 | 1 2 1 .o3.o4.o | * 12 | 0 4 | 0 2 2 -------------+-------+-------+------- x. .. .. | 2 0 | 24 * | 1 1 0 oo3oo4oo&#k | 1 1 | * 48 | 0 1 1 -------------+-------+-------+------- x.3o. .. | 3 0 | 3 0 | 8 * * x-{3} xo .. ..&#k | 2 1 | 1 2 | * 24 * xkk .. oK4Ko&#zk | 4 4 | 0 8 | * * 6 k-{8}
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