Acronym | dittec |
Name |
ditruncated cube, truncated truncated cube, expanded ambiated tic |
Circumradius | sqrt[(7+4 sqrt(2))y^{2}+(24+16 sqrt(2))y+(24+16 sqrt(2))]/2 |
Confer |
Truncation wrt. a non-regular polytope is meant to any instance of truncations on all vertices. For pre-images with different edge types however the ratio correlation of the remaining bits of those becomes arbitrary. Therefore tic cannot be truncated (within this stronger sense). Nonetheless the Conway operator of ambification (chosing the edge centers generally) clearly is applicable. And thus an expansion of that ambification could replace the usual expansion of the rectification here. This would result in 3 different edge sizes in the outcome polyhedron. That one here is scaled such so that the shorter specified one becomes unity. Then the larger specified edge will have size k=sqrt[2+sqrt(2)]. The third one would be the arbitrary expansion size y (corresponding to the arbitrary truncation depth). In fact, for y=0 this results again in retic, while y → ∞ results again in the pre-image tic (rescaled back down accordingly).
Incidence matrix according to Dynkin symbol
xo3yb4by&#zk → height = 0 k = x(8,2) = sqrt[2+sqrt(2)] = 1.847759 y > 0 (depending on truncation depth) b = y+2+sqrt(2) (pseudo) (k-laced tegum sum of x3y4b and o3b4y) o.3o.4o. | 48 * | 1 1 1 0 | 1 1 1 .o3.o4.o | * 24 | 0 0 2 1 | 0 1 2 -------------+-------+-------------+------- x. .. .. | 2 0 | 24 * * * | 1 1 0 x .. y. .. | 2 0 | * 24 * * | 1 0 1 y oo3oo4oo&#k | 1 1 | * * 48 * | 0 1 1 k .. .. .y | 0 2 | * * * 12 | 0 0 2 y -------------+-------+-------------+------- x.3y. .. | 6 0 | 3 3 0 0 | 8 * * (x,y)-{6} xo .. ..&#k | 2 1 | 1 0 2 0 | * 24 * xkk .. yb4by&#zk | 8 8 | 0 4 8 4 | * * 6 (y,k)-{16}
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