o x3o     
             
             
x o3o   x o3x

The 2 hex margin tet first oriented hin half, i.e. tetaf, then is being considered as tet atop gyrated tepe. If the top tet gets diminished down to its opposite face and the thereby induced cutting plane just scratches the other segmentoteron base tangentially, then this polyteron is obtained.

Incidence matrix according to Dynkin symbol

oxx oox3xoo&#x   → height(1,2) = height(1,3) = sqrt(5/12) = 0.645497
                   height(2,3) = sqrt(2/3) = 0.816497
                   height(1,23) = 1/2 ({3} || gyro tepe)
                   height(12,3) = 1/sqrt(2) = 0.707107 (pen || gyro trip)

o.. o..3o..    | 3 * * | 2 2  4 0 0 0 0 | 1 1 4  4 2 2 4 0 0 0 0 | 2 2 2 2 4 1 2 2 0 0 0 | 1 1 2 2 1 0
.o. .o.3.o.    | * 2 * | 0 3  0 1 3 0 0 | 0 3 3  6 0 0 0 3 3 0 0 | 3 1 6 3 3 0 0 0 3 1 0 | 1 3 3 1 0 1
..o ..o3..o    | * * 6 | 0 0  2 0 1 1 2 | 0 0 0  2 2 2 1 1 2 2 1 | 0 0 2 2 1 2 1 1 2 1 1 | 0 2 1 1 1 1
---------------+-------+----------------+------------------------+-----------------------+------------
... ... x..    | 2 0 0 | 3 *  * * * * * | 1 0 2  0 0 0 2 0 0 0 0 | 1 2 0 0 2 0 1 2 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 | 2 1 2 1 2 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 1 1 1 1 1 1 0 0 0 | 0 1 1 1 1 0
.x. ... ...    | 0 2 0 | * *  * 1 * * * | 0 3 0  0 0 0 0 3 0 0 0 | 3 0 6 0 0 0 0 0 3 0 0 | 1 3 3 0 0 1
.oo .oo3.oo&#x | 0 1 1 | * *  * * 6 * * | 0 0 0  2 0 0 0 1 2 0 0 | 0 0 2 2 1 0 0 0 2 1 0 | 0 2 1 1 0 1
..x ... ...    | 0 0 2 | * *  * * * 3 * | 0 0 0  0 2 0 0 1 0 2 0 | 0 0 2 0 0 2 1 0 2 0 1 | 0 2 1 0 1 1
... ..x ...    | 0 0 2 | * *  * * * * 6 | 0 0 0  0 0 1 0 0 1 1 1 | 0 0 0 1 0 1 0 1 1 1 1 | 0 1 0 1 1 1
---------------+-------+----------------+------------------------+-----------------------+------------
... o..3x..    | 3 0 0 | 3 0  0 0 0 0 0 | 1 * *  * * * * * * * * | 0 2 0 0 0 0 0 2 0 0 0 | 1 0 0 2 1 0
ox. ... ...&#x | 1 2 0 | 0 2  0 1 0 0 0 | * 3 *  * * * * * * * * | 2 0 2 0 0 0 0 0 0 0 0 | 1 1 2 0 0 0
... ... xo.&#x | 2 1 0 | 1 2  0 0 0 0 0 | * * 6  * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 0 | 1 0 1 1 0 0
ooo ooo3ooo&#x | 1 1 1 | 0 1  1 0 1 0 0 | * * * 12 * * * * * * * | 0 0 1 1 1 0 0 0 0 0 0 | 0 1 1 1 0 0
o.x ... ...&#x | 1 0 2 | 0 0  2 0 0 1 0 | * * *  * 6 * * * * * * | 0 0 1 0 0 1 1 0 0 0 0 | 0 1 1 0 1 0
... o.x ...&#x | 1 0 2 | 0 0  2 0 0 0 1 | * * *  * * 6 * * * * * | 0 0 0 1 0 1 0 1 0 0 0 | 0 1 0 1 1 0
... ... x.o&#x | 2 0 1 | 1 0  2 0 0 0 0 | * * *  * * * 6 * * * * | 0 0 0 0 1 0 1 1 0 0 0 | 0 0 1 1 1 0
.xx ... ...&#x | 0 2 2 | 0 0  0 1 2 1 0 | * * *  * * * * 3 * * * | 0 0 2 0 0 0 0 0 2 0 0 | 0 2 1 0 0 1
... .ox ...&#x | 0 1 2 | 0 0  0 0 2 0 1 | * * *  * * * * * 6 * * | 0 0 0 1 0 0 0 0 1 1 0 | 0 1 0 1 0 1
..x ..x ...    | 0 0 4 | 0 0  0 0 0 2 2 | * * *  * * * * * * 3 * | 0 0 0 0 0 1 0 0 1 0 1 | 0 1 0 0 1 1
... ..x3..o    | 0 0 3 | 0 0  0 0 0 0 3 | * * *  * * * * * * * 2 | 0 0 0 0 0 0 0 1 0 1 1 | 0 0 0 1 1 1
---------------+-------+----------------+------------------------+-----------------------+------------
ox. ... xo.&#x ♦ 2 2 0 | 1 4  0 1 0 0 0 | 0 2 2  0 0 0 0 0 0 0 0 | 3 * * * * * * * * * * | 1 0 1 0 0 0
... oo.3xo.&#x ♦ 3 1 0 | 3 3  0 0 0 0 0 | 1 0 3  0 0 0 0 0 0 0 0 | * 2 * * * * * * * * * | 1 0 0 1 0 0
oxx ... ...&#x ♦ 1 2 2 | 0 2  2 1 2 1 0 | 0 1 0  2 1 0 0 1 0 0 0 | * * 6 * * * * * * * * | 0 1 1 0 0 0
... oox ...&#x ♦ 1 1 2 | 0 1  2 0 2 0 1 | 0 0 0  2 0 1 0 0 1 0 0 | * * * 6 * * * * * * * | 0 1 0 1 0 0
... ... xoo&#x ♦ 2 1 1 | 1 2  2 0 1 0 0 | 0 0 1  2 0 0 1 0 0 0 0 | * * * * 6 * * * * * * | 0 0 1 1 0 0
o.x o.x ...&#x ♦ 1 0 4 | 0 0  4 0 0 2 2 | 0 0 0  0 2 2 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 1 0 | 0 0 0  0 2 0 2 0 0 0 0 | * * * * * * 3 * * * * | 0 0 1 0 1 0
... o.x3x.o&#x ♦ 3 0 3 | 3 0  6 0 0 0 3 | 1 0 0  0 0 3 3 0 0 0 1 | * * * * * * * 2 * * * | 0 0 0 1 1 0
.xx .ox ...&#x ♦ 0 2 4 | 0 0  0 1 4 2 2 | 0 0 0  0 0 0 0 2 2 1 0 | * * * * * * * * 3 * * | 0 1 0 0 0 1
... .ox3.oo&#x ♦ 0 1 3 | 0 0  0 0 3 0 3 | 0 0 0  0 0 0 0 0 3 0 1 | * * * * * * * * * 2 * | 0 0 0 1 0 1
..x ..x3..o    ♦ 0 0 6 | 0 0  0 0 0 3 6 | 0 0 0  0 0 0 0 0 0 3 2 | * * * * * * * * * * 1 | 0 0 0 0 1 1
---------------+-------+----------------+------------------------+-----------------------+------------
ox. oo.3xo.&#x ♦ 3 2 0 | 3 6  0 1 0 0 0 | 1 3 6  0 0 0 0 0 0 0 0 | 3 2 0 0 0 0 0 0 0 0 0 | 1 * * * * *
oxx oox ...&#x ♦ 1 2 4 | 0 2  4 1 4 2 2 | 0 1 0  4 2 2 0 2 2 1 0 | 0 0 2 2 0 1 0 0 1 0 0 | * 3 * * * *	
oxx ... xoo&#x ♦ 2 2 2 | 1 4  4 1 2 1 0 | 0 2 2  4 2 0 2 1 0 0 0 | 1 0 2 0 2 0 1 0 0 0 0 | * * 3 * * *
... oox3xoo&#x ♦ 3 1 3 | 3 3  6 0 3 0 3 | 1 0 3  6 0 3 3 0 3 0 1 | 0 1 0 3 3 0 0 1 0 1 0 | * * * 2 * *
o.x o.x3x.o&#x ♦ 3 0 6 | 3 0 12 0 0 3 6 | 1 0 0  0 6 6 6 0 0 3 2 | 0 0 0 0 0 3 3 2 0 0 1 | * * * * 1 *
.xx .ox3.oo&#x ♦ 0 2 6 | 0 0  0 1 6 3 6 | 0 0 0  0 0 0 0 3 6 3 2 | 0 0 0 0 0 0 0 0 3 2 1 | * * * * * 1