Acronym ditetaf (alt.: traltepe, penaltrip)
Name diminished tetaf,
triangle atop gyrated tepe,
pen atop gyrated trip,
(edge,perp triangle,gyro trip)-trigonic
Circumradius sqrt(5/8) = 0.790569
Lace city
in approx. ASCII-art
   o x3o     
             
             
x o3o   x o3x
Confer
uniform relative:
hin  
related segmentotera:
tetaf  
general polytopal classes:
segmentotera   lace simplices  

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

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