Acronym ...
Name Waterman polyhedron number 8 wrt. primitive cubic lattice C3 centered at a lattice point,
Waterman polyhedron number 4 wrt. face-centered cubic lattice A3 centered at a deep hole
 
 
Circumradius 3/sqrt(2) = 2.121320
Face vector 30, 84, 56

The unit here was chosen as the root of A3. (When using the root of C3, then all measures would have to be scaled up by an additional factor of sqrt(2).)

By the very definition of Waterman polyhedra, not necessarily all vertices are on the same sphere. However in here both the 6 dark purple vertices and the 24 violet vertices belong to the same radius.


Incidence matrix according to Dynkin symbol

do3ox4oq&#zh   → height = 0, where d = 3 (pseudo)
(tegum sum of d-oct and (x,q)-tic)

o.3o.4o.    | 6  * |  8  0  0 |  4  4 0  (dark purple)
.o3.o4.o    | * 24 |  2  2  1 |  2  2 1  (violet)
------------+------+----------+--------
oo3oo4oo&#h | 1  1 | 48  *  * |  1  1 0  h
.. .x ..    | 0  2 |  * 24  * |  1  0 1  x
.. .. .q    | 0  2 |  *  * 12 |  0  2 0  q
------------+------+----------+--------
.. ox ..&#h | 1  2 |  2  1  0 | 24  * *
.. .. oq&#h | 1  2 |  2  0  1 |  * 24 *
.o3.x ..    | 0  3 |  0  3  0 |  *  * 8

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