Note that the acronym here was chosen to be "tutrippapy" for this tutrip pyramid. In contrast, "tutrippy" then refers to the external 2 trippy blend instead. Nonetheless this polychoron can likewise be considered an internal 2 trippy blend as well. In fact, in here one trip each blends into a tutrip, whereas in the external one a squippy each would blend into an oct.

Incidence matrix according to Dynkin symbol

pt || ( 2{2} || pseudo {4} )   → height(1,23) = sqrt(5/12) = 0.645497

      o.. o..      | 1 * * ♦ 4 4 0 0 0 | 2 8 4 0 0 | 4 4 0
both( .o. .o.    ) | * 4 * | 1 0 1 2 0 | 1 2 0 2 1 | 2 1 1
      ..o ..o      | * * 4 | 0 1 0 2 2 | 0 2 2 2 2 | 2 2 1
-------------------+-------+-----------+-----------+------
both( oo. oo.&#x ) | 1 1 0 | 4 * * * * | 1 2 0 0 0 | 2 1 0
      o.o o.o&#x   | 1 0 1 | * 4 * * * | 0 2 2 0 0 | 2 2 0
both( .x. ...    ) | 0 2 0 | * * 2 * * | 1 0 0 2 0 | 2 0 1
both( .oo .oo&#x ) | 0 1 1 | * * * 8 * | 0 1 0 1 1 | 1 1 1
      ..x ...    & | 0 0 2 | * * * * 4 | 0 0 1 1 1 | 1 1 1  (identified)
-------------------+-------+-----------+-----------+------
both( ox. ...&#x ) | 1 2 0 | 2 0 1 0 0 | 2 * * * * | 2 0 0
both( ooo ooo&#x ) | 1 1 1 | 1 1 0 1 0 | * 8 * * * | 1 1 0
      o.x ...&#x & | 1 0 2 | 0 2 0 0 1 | * * 4 * * | 1 1 0
both( .xx ...&#x ) | 0 2 2 | 0 0 1 2 1 | * * * 4 * | 1 0 1
both( ... .ox&#x ) | 0 1 2 | 0 0 0 2 1 | * * * * 4 | 0 1 1
-------------------+-------+-----------+-----------+------
both( oxx ...&#x ) ♦ 1 2 2 | 2 2 1 2 1 | 1 2 1 1 0 | 4 * *
both( ... oox&#x ) ♦ 1 1 2 | 1 2 0 2 1 | 0 2 1 0 1 | * 4 *
both( .xx .ox&#x ) ♦ 0 4 4 | 0 0 2 8 4 | 0 0 0 4 4 | * * 1

reduced( oxx4/2oox&#x , by ..x4/2..x )   → height(1,23) = sqrt(5/12) = 0.645497
                                           height(1,2) = height(2,3) = sqrt(3)/2 = 0.866025
                                           height(1,3) = 1/sqrt(2) = 0.707107

         o..4/2o..      | 1 * * ♦ 4 4 0 0 0 | 2 8 4 0 0 | 4 4 0
         .o.4/2.o.      | * 4 * | 1 0 1 2 0 | 1 2 0 2 1 | 2 1 1
         ..o4/2..o      | * * 4 | 0 1 0 2 2 | 0 2 2 2 2 | 2 2 1
------------------------+-------+-----------+-----------+------
         oo.4/2oo.&#x   | 1 1 0 | 4 * * * * | 1 2 0 0 0 | 2 1 0
         o.o4/2o.o&#x   | 1 0 1 | * 4 * * * | 0 2 2 0 0 | 2 2 0
         .x.   ...      | 0 2 0 | * * 2 * * | 1 0 0 2 0 | 2 0 1
         .oo4/2.oo&#x   | 0 1 1 | * * * 8 * | 0 1 0 1 1 | 1 1 1
reduced( ..x   ...  & ) | 0 0 2 | * * * * 4 | 0 0 1 1 1 | 1 1 1
------------------------+-------+-----------+-----------+------
         ox.   ...&#x   | 1 2 0 | 2 0 1 0 0 | 2 * * * * | 2 0 0
         ooo4/2ooo&#x   | 1 1 1 | 1 1 0 1 0 | * 8 * * * | 1 1 0
         .xx   ...&#x   | 0 2 2 | 0 0 1 2 1 | * * * 4 * | 1 0 1
         ...   .ox&#x   | 0 1 2 | 0 0 0 2 1 | * * * * 4 | 0 1 1
------------------------+-------+-----------+-----------+------
         oxx   ...&#x   ♦ 1 2 2 | 2 2 1 2 1 | 1 2 1 1 0 | 4 * *
         ...   oox&#x   ♦ 1 1 2 | 1 2 0 2 1 | 0 2 1 0 1 | * 4 *
reduced( .xx4/2.ox&#x ) ♦ 0 4 4 | 0 0 2 8 4 | 0 0 0 4 4 | * * 1