o o3x  
              
              
              
x o3x    x x3o

This wedge of dot can be obtained from its tet-first half, tetaope, as a diminishing. In fact the cutting hyperplane rasps the top tet from one of its tips down to its opposite triangle, whereas at the opposite base it just scratches tangentially, that is, the ope there remains unchanged.

None the same it well can be extrapolated towards any general N-gonal symmetry other than just 3, then resulting in (N-gon, N-p, gyro N-p)-trigonic.

Note that in here the triddip indeed is taken in gyro-para orientation. There is an other polytope, also having a trip atop some triddip, but where this mutual orientation is taken gyro-perp instead. For sure, it therefore is no longer a polyteron, rather it becomes a polypeton instead. That one then would be tripal triddip.

Incidence matrix according to Dynkin symbol

oxx oox3xxo&#x   → height(1,2) = sqrt(3)/2 = 0.866025
                   height(1,3) = sqrt(5/12) = 0.645497
                   height(2,3) = sqrt(2/3) = 0.816497

o.. o..3o..    | 3 * * | 2 2  4 0 0  0 0 0 | 1 1 4  4 2 2 4 0 0 0 0 0 0 0 | 2 2 2 2 4 1 2 2 0 0 0 0 0 | 1 1 2 2 1 0
.o. .o.3.o.    | * 6 * | 0 1  0 1 2  2 0 0 | 0 1 2  2 0 0 0 2 1 2 1 2 0 0 | 2 1 2 1 2 0 0 0 1 1 2 1 0 | 1 1 2 1 0 1
..o ..o3..o    | * * 6 | 0 0  2 0 0  2 1 2 | 0 0 0  2 2 2 1 0 0 2 2 1 2 1 | 0 0 2 2 1 2 1 1 0 2 1 1 1 | 0 2 1 1 1 1
---------------+-------+-------------------+------------------------------+---------------------------+------------
... ... x..    | 2 0 0 | 3 *  * * *  * * * | 1 0 2  0 0 0 2 0 0 0 0 0 0 0 | 1 2 0 0 2 0 1 2 0 0 0 0 0 | 1 0 1 2 1 0
oo. oo.3oo.&#x | 1 1 0 | * 6  * * *  * * * | 0 1 2  2 0 0 0 0 0 0 0 0 0 0 | 2 1 2 1 2 0 0 0 0 0 0 0 0 | 1 1 2 1 0 0
o.o o.o3o.o&#x | 1 0 1 | * * 12 * *  * * * | 0 0 0  1 1 1 1 0 0 0 0 0 0 0 | 0 0 1 1 1 1 1 1 0 0 0 0 0 | 0 1 1 1 1 0
.x. ... ...    | 0 2 0 | * *  * 3 *  * * * | 0 1 0  0 0 0 0 2 0 2 0 0 0 0 | 2 0 2 0 0 0 0 0 1 1 2 0 0 | 1 1 2 0 0 1
... ... .x.    | 0 2 0 | * *  * * 6  * * * | 0 0 1  0 0 0 0 1 1 0 0 1 0 0 | 1 1 0 0 1 0 0 0 1 0 1 1 0 | 1 0 1 1 0 1
.oo .oo3.oo&#x | 0 1 1 | * *  * * * 12 * * | 0 0 0  1 0 0 0 0 0 1 1 1 0 0 | 0 0 1 1 1 0 0 0 0 1 1 1 0 | 0 1 1 1 0 1
..x ... ...    | 0 0 2 | * *  * * *  * 3 * | 0 0 0  0 2 0 0 0 0 2 0 0 2 0 | 0 0 2 0 0 2 1 0 0 2 1 0 1 | 0 2 1 0 1 1
... ..x ...    | 0 0 2 | * *  * * *  * * 6 | 0 0 0  0 0 1 0 0 0 0 1 0 1 1 | 0 0 0 1 0 1 0 1 0 1 0 1 1 | 0 1 0 1 1 1
---------------+-------+-------------------+------------------------------+---------------------------+------------
... o..3x..    | 3 0 0 | 3 0  0 0 0  0 0 0 | 1 * *  * * * * * * * * * * * | 0 2 0 0 0 0 0 2 0 0 0 0 0 | 1 0 0 2 1 0
ox. ... ...&#x | 1 2 0 | 0 2  0 1 0  0 0 0 | * 3 *  * * * * * * * * * * * | 2 0 2 0 0 0 0 0 0 0 0 0 0 | 1 1 2 0 0 0
... ... xx.&#x | 2 2 0 | 1 2  0 0 1  0 0 0 | * * 6  * * * * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0
ooo ooo3ooo&#x | 1 1 1 | 0 1  1 0 0  1 0 0 | * * * 12 * * * * * * * * * * | 0 0 1 1 1 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0
o.x ... ...&#x | 1 0 2 | 0 0  2 0 0  0 1 0 | * * *  * 6 * * * * * * * * * | 0 0 1 0 0 1 1 0 0 0 0 0 0 | 0 1 1 0 1 0
... o.x ...&#x | 1 0 2 | 0 0  2 0 0  0 0 1 | * * *  * * 6 * * * * * * * * | 0 0 0 1 0 1 0 1 0 0 0 0 0 | 0 1 0 1 1 0
... ... x.o&#x | 2 0 1 | 1 0  2 0 0  0 0 0 | * * *  * * * 6 * * * * * * * | 0 0 0 0 1 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0
.x. ... .x.    | 0 4 0 | 0 0  0 2 2  0 0 0 | * * *  * * * * 3 * * * * * * | 1 0 0 0 0 0 0 0 1 0 1 0 0 | 1 0 1 0 0 1
... .o.3.x.    | 0 3 0 | 0 0  0 0 3  0 0 0 | * * *  * * * * * 2 * * * * * | 0 1 0 0 0 0 0 0 1 0 0 1 0 | 1 0 0 1 0 1
.xx ... ...&#x | 0 2 2 | 0 0  0 1 0  2 1 0 | * * *  * * * * * * 6 * * * * | 0 0 1 0 0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
... .ox ...&#x | 0 1 2 | 0 0  0 0 0  2 0 1 | * * *  * * * * * * * 6 * * * | 0 0 0 1 0 0 0 0 0 1 0 1 0 | 0 1 0 1 0 1
... ... .xo&#x | 0 2 1 | 0 0  0 0 1  2 0 0 | * * *  * * * * * * * * 6 * * | 0 0 0 0 1 0 0 0 0 0 1 1 0 | 0 0 1 1 0 1
..x ..x ...    | 0 0 4 | 0 0  0 0 0  0 2 2 | * * *  * * * * * * * * * 3 * | 0 0 0 0 0 1 0 0 0 1 0 0 1 | 0 1 0 0 1 1
... ..x3..o    | 0 0 3 | 0 0  0 0 0  0 0 3 | * * *  * * * * * * * * * * 2 | 0 0 0 0 0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
---------------+-------+-------------------+------------------------------+---------------------------+------------
ox. ... xx.&#x ♦ 2 4 0 | 1 4  0 2 2  0 0 0 | 0 2 2  0 0 0 0 1 0 0 0 0 0 0 | 3 * * * * * * * * * * * * | 1 0 1 0 0 0
... oo.3xx.&#x ♦ 3 3 0 | 3 3  0 0 3  0 0 0 | 1 0 3  0 0 0 0 0 1 0 0 0 0 0 | * 2 * * * * * * * * * * * | 1 0 0 1 0 0
oxx ... ...&#x ♦ 1 2 2 | 0 2  2 1 0  2 1 0 | 0 1 0  2 1 0 0 0 0 1 0 0 0 0 | * * 6 * * * * * * * * * * | 0 1 1 0 0 0
... oox ...&#x ♦ 1 1 2 | 0 1  2 0 0  2 0 1 | 0 0 0  2 0 1 0 0 0 0 1 0 0 0 | * * * 6 * * * * * * * * * | 0 1 0 1 0 0
... ... xxo&#x ♦ 2 2 1 | 1 2  2 0 1  2 0 0 | 0 0 1  2 0 0 1 0 0 0 0 1 0 0 | * * * * 6 * * * * * * * * | 0 0 1 1 0 0
o.x o.x ...&#x ♦ 1 0 4 | 0 0  4 0 0  0 2 2 | 0 0 0  0 2 2 0 0 0 0 0 0 1 0 | * * * * * 3 * * * * * * * | 0 1 0 0 1 0
o.x ... x.o&#x ♦ 2 0 2 | 1 0  4 0 0  0 1 0 | 0 0 0  0 2 0 2 0 0 0 0 0 0 0 | * * * * * * 3 * * * * * * | 0 0 1 0 1 0
... o.x3x.o&#x ♦ 3 0 3 | 3 0  6 0 0  0 0 3 | 1 0 0  0 0 3 3 0 0 0 0 0 0 1 | * * * * * * * 2 * * * * * | 0 0 0 1 1 0
.x. .o.3.x.    ♦ 0 6 0 | 0 0  0 3 6  0 0 0 | 0 0 0  0 0 0 0 3 2 0 0 0 0 0 | * * * * * * * * 1 * * * * | 1 0 0 0 0 1
.xx .ox ...&#x ♦ 0 2 4 | 0 0  0 1 0  4 2 2 | 0 0 0  0 0 0 0 0 0 2 2 0 1 0 | * * * * * * * * * 3 * * * | 0 1 0 0 0 1
.xx ... .xo&#x ♦ 0 4 2 | 0 0  0 2 2  4 1 0 | 0 0 0  0 0 0 0 1 0 2 0 2 0 0 | * * * * * * * * * * 3 * * | 0 0 1 0 0 1
... .ox3.xo&#x ♦ 0 3 3 | 0 0  0 0 3  6 0 3 | 0 0 0  0 0 0 0 0 1 0 3 3 0 1 | * * * * * * * * * * * 2 * | 0 0 0 1 0 1
..x ..x3..o    ♦ 0 0 6 | 0 0  0 0 0  0 3 6 | 0 0 0  0 0 0 0 0 0 0 0 0 3 2 | * * * * * * * * * * * * 1 | 0 0 0 0 1 1
---------------+-------+-------------------+------------------------------+---------------------------+------------
ox. oo.3xx.&#x ♦ 3 6 0 | 3 6  0 3 6  0 0 0 | 1 3 6  0 0 0 0 3 2 0 0 0 0 0 | 3 2 0 0 0 0 0 0 1 0 0 0 0 | 1 * * * * *
oxx oox ...&#x ♦ 1 2 4 | 0 2  4 1 0  4 2 2 | 0 1 0  4 2 2 0 0 0 2 2 0 1 0 | 0 0 2 2 0 1 0 0 0 1 0 0 0 | * 3 * * * *
oxx ... xxo&#x ♦ 2 4 2 | 1 4  4 2 2  4 1 0 | 0 2 2  4 2 0 2 1 0 2 0 2 0 0 | 1 0 2 0 2 0 1 0 0 0 1 0 0 | * * 3 * * *
... oox3xxo&#x ♦ 3 3 3 | 3 3  6 0 3  6 0 3 | 1 0 3  6 0 3 3 0 1 0 3 3 0 1 | 0 1 0 3 3 0 0 1 0 0 0 1 0 | * * * 2 * *
o.x o.x3x.o&#x ♦ 3 0 6 | 3 0 12 0 0  0 3 6 | 1 0 0  0 6 6 6 0 0 0 0 0 3 2 | 0 0 0 0 0 3 3 2 0 0 0 0 1 | * * * * 1 *
.xx .ox3.xo&#x ♦ 0 6 6 | 0 0  0 3 6 12 3 6 | 0 0 0  0 0 0 0 3 2 6 6 6 3 2 | 0 0 0 0 0 0 0 0 1 3 3 2 1 | * * * * * 1