Acronym	retepe (alt.: amtepe)
Name	rectified/ambified tepe
	©
Circumradius	sqrt(3/2) = 1.224745
Face vector	16, 48, 46, 14
Confer	ambification pre-image: tepe
External links

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 tepe as a pre-image these intersection points might differ on its 2 edge types. Therefore tepe 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 polychoron. That one here is scaled such so that the smaller one becomes unity. Then the longer edge will have size q = sqrt(2).

The non-polar triangles {(t,T,T)} have vertex angles t = arccos(3/4) = 41.409622° resp. T = arccos[1/sqrt(8)] = 69.295189°.

All u = 2 edges, used in the below descriptions, only qualify as pseudo edges wrt. the full polychoron.

Incidence matrix according to Dynkin symbol

uo3ox3oo ou&#zq   → height = 0

o.3o.3o. o.     | 4  * |  6  0 | 3  6 0 0 | 3 2 0
.o3.o3.o .o     | * 12 |  2  4 | 1  4 2 2 | 2 2 1
----------------+------+-------+----------+------
oo3oo3oo oo&#q  | 1  1 | 24  * | 1  2 0 0 | 2 1 0  q
.. .x .. ..     | 0  2 |  * 24 | 0  1 1 1 | 1 1 1  x
----------------+------+-------+----------+------
uo .. .. ou&#zq | 2  2 |  4  0 | 6  * * * | 2 0 0  q-{4}
.. ox .. ..&#q  | 1  2 |  2  1 | * 24 * * | 1 1 0  {(t,T,T)}
.o3.x .. ..     | 0  3 |  0  3 | *  * 8 * | 1 0 1
.. .x3.o ..     | 0  3 |  0  3 | *  * * 8 | 0 1 1
----------------+------+-------+----------+------
uo3ox .. ou&#zq ♦ 3  6 | 12  6 | 3  6 2 0 | 4 * *
.. ox3oo ..&#q  ♦ 1  3 |  3  3 | 0  3 0 1 | * 8 *
.o3.x3.o ..     ♦ 0  6 |  0 12 | 0  0 4 4 | * * 2

ouo3xox3ooo&#qt   → both heights = 1

o..3o..3o..     | 6 * * |  4  2  0  0 | 2 2 1  4  0 0 0 | 1 2 2 0 0
.o.3.o.3.o.     | * 4 * |  0  3  3  0 | 0 0 3  3  3 0 0 | 0 3 1 1 0
..o3..o3..o     | * * 6 |  0  0  2  4 | 0 0 1  0  4 2 2 | 0 2 0 2 1
----------------+-------+-------------+-----------------+----------
... x.. ...     | 2 0 0 | 12  *  *  * | 1 1 0  1  0 0 0 | 1 1 1 0 0
oo.3oo.3oo.&#q  | 1 1 0 |  * 12  *  * | 0 0 1  2  0 0 0 | 0 2 1 0 0
.oo3.oo3.oo&#q  | 0 1 1 |  *  * 12  * | 0 0 1  0  2 0 0 | 0 2 0 1 0
... ..x ...     | 0 0 2 |  *  *  * 12 | 0 0 0  0  1 1 1 | 0 1 0 1 1
----------------+-------+-------------+-----------------+----------
o..3x.. ...     | 3 0 0 |  3  0  0  0 | 4 * *  *  * * * | 1 1 0 0 0
... x..3o..     | 3 0 0 |  3  0  0  0 | * 4 *  *  * * * | 1 0 1 0 0
ouo ... ...&#qt | 1 2 1 |  0  2  2  0 | * * 6  *  * * * | 0 2 0 0 0
... xo. ...&#q  | 2 1 0 |  1  2  0  0 | * * * 12  * * * | 0 1 1 0 0
... .ox ...&#q  | 0 1 2 |  0  0  2  1 | * * *  * 12 * * | 0 1 0 1 0
..o3..x ...     | 0 0 3 |  0  0  0  3 | * * *  *  * 4 * | 0 1 0 0 1
... ..x3..o     | 0 0 3 |  0  0  0  3 | * * *  *  * * 4 | 0 0 0 1 1
----------------+-------+-------------+-----------------+----------
o..3x..3o..     ♦ 6 0 0 | 12  0  0  0 | 4 4 0  0  0 0 0 | 1 * * * *
ouo3xox ...&#qt ♦ 3 3 3 |  3  6  6  3 | 1 0 3  3  3 1 0 | * 4 * * *
... xo.3oo.&#q  ♦ 3 1 0 |  3  3  0  0 | 0 1 0  3  0 0 0 | * * 4 * *
... .ox3.oo&#q  ♦ 0 1 3 |  0  0  3  3 | 0 0 0  0  3 0 1 | * * * 4 *
..o3..x3..o     ♦ 0 0 6 |  0  0  0 12 | 0 0 0  0  0 4 4 | * * * * 1