Acronym retdip (old: retriddip) Name rectified triddip Circumradius sqrt(5/3) = 1.290994 Lace cityin approx. ASCII-art x3o o3u o3u x3o o3u x3o Confer more general variants: case 0 < b:a < 1/2 or 2 < b:a < ∞  /  this case b:a = 1/2 or b:a = 2  /  case 1/2 < b:a < 2   with esp. case b:a = 1 general polytopal classes: isogonal Externallinks

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 triddip all edges belong to a single orbit of symmetry, i.e. rectification clearly is applicable, without any recourse to Conway's ambification (chosing the former edge centers generally). None the less, wrt. the individual cells of the pre-image, there an ambification is possible only, i.e. trip cannot be rectified (within this stronger sense).

Still, because the pre-image uses different polygonal faces, this would result in 2 different edge sizes in the outcome polychoron. That one here is scaled such so that the shorter one becomes unity. Then the larger edge will have size q=sqrt(2).

No uniform realisation is possible for any of those ao3ob bo3oa&#zc. Even so all are isogonal.

Incidence matrix according to Dynkin symbol

xo3ou uo3ox&#zq - height = 0

o.3o. o.3o.     & | 18 |  2  4 | 1  6 2 | 2 3
------------------+----+-------+--------+----
x. .. .. ..     & |  2 | 18  * | 1  2 0 | 1 2  x
oo3oo oo3oo&#q    |  2 |  * 36 | 0  2 1 | 1 2  q
------------------+----+-------+--------+----
x.3o. .. ..     & |  3 |  3  0 | 6  * * | 0 2  x-{3}
xo .. .. ..&#q  & |  3 |  1  2 | * 36 * | 1 1  xqq
.. ou uo ..&#zq   |  4 |  0  4 | *  * 9 | 0 2  q-{4}
------------------+----+-------+--------+----
xo .. .. ox&#q      4 |  2  4 | 0  4 0 | 9 *
xo3ou uo ..&#zq &   9 |  6 12 | 2  6 3 | * 6