The corresponding 3/2-cuploid, i.e. withdrawing the exceptional Grünbaumian bottom base (by identification of the pairwise coincident bottom edges), would be better known as tetrahemitetrahedron.

Incidence matrix according to Dynkin symbol

xx3/2ox&#x   → height = sqrt(2/3) = 0.816497
({3} || dual {6/2})

o.3/2o.    | 3 * | 2 2 0 0 | 1 2 1 0
.o3/2.o    | * 6 | 0 1 1 1 | 0 1 1 1
-----------+-----+---------+--------
x.   ..    | 2 0 | 3 * * * | 1 1 0 0
oo3/2oo&#x | 1 1 | * 6 * * | 0 1 1 0
.x   ..    | 0 2 | * * 3 * | 0 1 0 1
..   .x    | 0 2 | * * * 3 | 0 0 1 1
-----------+-----+---------+--------
x.3/2o.    | 3 0 | 3 0 0 0 | 1 * * *
xx   ..&#x | 2 2 | 1 2 1 0 | * 3 * *
..   ox&#x | 1 2 | 0 2 0 1 | * * 3 *
.x3/2.x    | 0 6 | 0 0 3 3 | * * * 1