The unit here was chosen as the root of A₃.

By the very definition of Waterman polyhedra, not necessarily all vertices are on the same sphere. However in here both the 4 vertices of the d-scaled tet layer and the other 12 vertices of the inverted (x,u)-tut layer belong to the same radius.

Incidence matrix according to Dynkin symbol

ox3ou3do&#zh   → height = 0, where d = 3 (pseudo)
(tegum sum of d-tet and inverted (x,u)-tut)

o.3o.3o.    | 4  * |  6 0  0 |  3  3 0
.o3.o3.o    | * 12 |  2 1  2 |  2  2 1
------------+------+---------+--------
oo3oo3oo&#h | 1  1 | 24 *  * |  1  1 0  h
.x .. ..    | 0  2 |  * 6  * |  2  0 0  x
.. .u ..    | 0  2 |  * * 12 |  0  1 1  u
------------+------+---------+--------
ox .. ..&#h | 1  2 |  2 1  0 | 12  * *
.. ou ..&#h | 1  2 |  2 0  1 |  * 12 *
.. .u3.o    | 0  3 |  0 0  3 |  *  * 4