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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