Acronym retoe (alt.: amtoe)
Name rectified/ambiated truncated octahedron
 
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Circumradius 3/sqrt(2) = 2.121320

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 toe 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 b = sqrt(3/2).


Incidence matrix according to Dynkin symbol

xo4oa3ao&#zb   → height = 0
                 a = 3/sqrt(2) = 2.121320 (pseudo)
                 b = sqrt(3/2) = 1.224745
(b-laced tegum sum of (a,x)-sirco and a-co)

o.4o.3o.     | 24  * |  2  2 | 1  2 1
.o4.o3.o     |  * 12 |  0  4 | 0  2 2
-------------+-------+-------+-------
x. .. ..     |  2  0 | 24  * | 1  1 0  x
oo4oo3oo&#b  |  1  1 |  * 48 | 0  1 1  b
-------------+-------+-------+-------
x.4o. ..     |  4  0 |  4  0 | 6  * *  x-{4}
xo .. ..&#b  |  2  1 |  1  2 | * 24 *  xbb
.. oa3ao&#zb |  3  3 |  0  6 | *  * 8  b-{6}

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