Acronym tedrix
Name tridiminished rectified hexateron,
lace simplex of 3 mutually orthogonal squares
Circumradius sqrt(2/3) = 0.816497
Lace city
in approx. ASCII-art
  T                 
            T=tet   
T   4       4=square
Confer
uniform relative:
rix  
general polytopal classes:
segmentotera   scaliform  

Incidence matrix according to Dynkin symbol

xxo2xox2oxx&#x   → all 3 mutual heights = 1/sqrt(2) = 0.707107
({4} || ortho tepe   → height = sqrt(3/8) = 0.612372)

o..2o..2o..    | 4 * * | 1 1 2 2 0 0 0 0 0 | 1 2 2 1 2 2 1 2 0 0 0 0 0 | 2 1 1 2 1 1 2 2 1 0 0 0 | 1 1 2 1 1 0
.o.2.o.2.o.    | * 4 * | 0 0 2 0 1 1 2 0 0 | 0 2 1 2 0 0 0 2 1 2 1 2 0 | 1 2 1 0 0 0 2 1 2 1 2 1 | 1 0 1 2 1 1
..o2..o2..o    | * * 4 | 0 0 0 2 0 0 2 1 1 | 0 0 0 0 1 2 2 2 0 1 2 2 1 | 0 0 0 1 1 2 1 2 2 1 1 2 | 0 1 1 1 2 1
---------------+-------+-------------------+---------------------------+-------------------------+------------
x.. ... ...    | 2 0 0 | 2 * * * * * * * * | 1 2 0 0 2 0 0 0 0 0 0 0 0 | 2 1 0 2 1 0 2 0 0 0 0 0 | 1 1 2 1 0 0
... x.. ...    | 2 0 0 | * 2 * * * * * * * | 1 0 2 0 0 2 0 0 0 0 0 0 0 | 2 0 1 2 0 1 0 2 0 0 0 0 | 1 1 2 0 1 0
oo.2oo.2oo.&#x | 1 1 0 | * * 8 * * * * * * | 0 1 1 1 0 0 0 1 0 0 0 0 0 | 1 1 1 0 0 0 1 1 1 0 0 0 | 1 0 1 1 1 0
o.o2o.o2o.o&#x | 1 0 1 | * * * 8 * * * * * | 0 0 0 0 1 1 1 1 0 0 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 | * * * * 2 * * * * | 0 2 0 0 0 0 0 0 1 2 0 0 0 | 1 2 0 0 0 0 2 0 0 1 2 0 | 1 0 1 2 0 1
... ... .x.    | 0 2 0 | * * * * * 2 * * * | 0 0 0 2 0 0 0 0 1 0 0 2 0 | 0 2 1 0 0 0 0 0 2 0 2 1 | 1 0 0 2 1 1
.oo2.oo2.oo&#x | 0 1 1 | * * * * * * 8 * * | 0 0 0 0 0 0 0 1 0 1 1 1 0 | 0 0 0 0 0 0 1 1 1 1 1 1 | 0 0 1 1 1 1
... ..x ...    | 0 0 2 | * * * * * * * 2 * | 0 0 0 0 0 2 0 0 0 0 2 0 1 | 0 0 0 1 0 2 0 2 0 1 0 2 | 0 1 1 0 2 1
... ... ..x    | 0 0 2 | * * * * * * * * 2 | 0 0 0 0 0 0 2 0 0 0 0 2 1 | 0 0 0 0 1 2 0 0 2 0 1 2 | 0 1 0 1 2 1
---------------+-------+-------------------+---------------------------+-------------------------+------------
x.. x.. ...    | 4 0 0 | 2 2 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * | 2 0 0 2 0 0 0 0 0 0 0 0 | 1 1 2 0 0 0
xx. ... ...&#x | 2 2 0 | 1 0 2 0 1 0 0 0 0 | * 4 * * * * * * * * * * * | 1 1 0 0 0 0 1 0 0 0 0 0 | 1 0 1 1 0 0
... xo. ...&#x | 2 1 0 | 0 1 2 0 0 0 0 0 0 | * * 4 * * * * * * * * * * | 1 0 1 0 0 0 0 1 0 0 0 0 | 1 0 1 0 1 0
... ... ox.&#x | 1 2 0 | 0 0 2 0 0 1 0 0 0 | * * * 4 * * * * * * * * * | 0 1 1 0 0 0 0 0 1 0 0 0 | 1 0 0 1 1 0
x.o ... ...&#x | 2 0 1 | 1 0 0 2 0 0 0 0 0 | * * * * 4 * * * * * * * * | 0 0 0 1 1 0 1 0 0 0 0 0 | 0 1 1 1 0 0
... x.x ...&#x | 2 0 2 | 0 1 0 2 0 0 0 1 0 | * * * * * 4 * * * * * * * | 0 0 0 1 0 1 0 1 0 0 0 0 | 0 1 1 0 1 0
... ... o.x&#x | 1 0 2 | 0 0 0 2 0 0 0 0 1 | * * * * * * 4 * * * * * * | 0 0 0 0 1 1 0 0 1 0 0 0 | 0 1 0 1 1 0
ooo2ooo2ooo&#x | 1 1 1 | 0 0 1 1 0 0 1 0 0 | * * * * * * * 8 * * * * * | 0 0 0 0 0 0 1 1 1 0 0 0 | 0 0 1 1 1 0
.x. ... .x.    | 0 4 0 | 0 0 0 0 2 2 0 0 0 | * * * * * * * * 1 * * * * | 0 2 0 0 0 0 0 0 0 0 2 0 | 1 0 0 2 0 1
.xo ... ...&#x | 0 2 1 | 0 0 0 0 1 0 2 0 0 | * * * * * * * * * 4 * * * | 0 0 0 0 0 0 1 0 0 1 1 0 | 0 0 1 1 0 1
... .ox ...&#x | 0 1 2 | 0 0 0 0 0 0 2 1 0 | * * * * * * * * * * 4 * * | 0 0 0 0 0 0 0 1 0 1 0 1 | 0 0 1 0 1 1
... ... .xx&#x | 0 2 2 | 0 0 0 0 0 1 2 0 1 | * * * * * * * * * * * 4 * | 0 0 0 0 0 0 0 0 1 0 1 1 | 0 0 0 1 1 1
... ..x ..x    | 0 0 4 | 0 0 0 0 0 0 0 2 2 | * * * * * * * * * * * * 1 | 0 0 0 0 0 2 0 0 0 0 0 2 | 0 1 0 0 2 1
---------------+-------+-------------------+---------------------------+-------------------------+------------
xx. xo. ...&#x  4 2 0 | 2 2 4 0 1 0 0 0 0 | 1 2 2 0 0 0 0 0 0 0 0 0 0 | 2 * * * * * * * * * * * | 1 0 1 0 0 0
xx. ... ox.&#x  2 4 0 | 1 0 4 0 2 2 0 0 0 | 0 2 0 2 0 0 0 0 1 0 0 0 0 | * 2 * * * * * * * * * * | 1 0 0 1 0 0
... xo. ox.&#x  2 2 0 | 0 1 4 0 0 1 0 0 0 | 0 0 2 2 0 0 0 0 0 0 0 0 0 | * * 2 * * * * * * * * * | 1 0 0 0 1 0
x.o x.x ...&#x  4 0 2 | 2 2 0 4 0 0 0 1 0 | 1 0 0 0 2 2 0 0 0 0 0 0 0 | * * * 2 * * * * * * * * | 0 1 1 0 0 0
x.o ... o.x&#x  2 0 2 | 1 0 0 4 0 0 0 0 1 | 0 0 0 0 2 0 2 0 0 0 0 0 0 | * * * * 2 * * * * * * * | 0 1 0 1 0 0
... x.x o.x&#x  2 0 4 | 0 1 0 4 0 0 0 2 2 | 0 0 0 0 0 2 2 0 0 0 0 0 1 | * * * * * 2 * * * * * * | 0 1 0 0 1 0
xxo ... ...&#x  2 2 1 | 1 0 2 2 1 0 2 0 0 | 0 1 0 0 1 0 0 2 0 1 0 0 0 | * * * * * * 4 * * * * * | 0 0 1 1 0 0
... xox ...&#x  2 1 2 | 0 1 2 2 0 0 2 1 0 | 0 0 1 0 0 1 0 2 0 0 1 0 0 | * * * * * * * 4 * * * * | 0 0 1 0 1 0
... ... oxx&#x  1 2 2 | 0 0 2 2 0 1 2 0 1 | 0 0 0 1 0 0 1 2 0 0 0 1 0 | * * * * * * * * 4 * * * | 0 0 0 1 1 0
.xo .ox ...&#x  0 2 2 | 0 0 0 0 1 0 4 1 0 | 0 0 0 0 0 0 0 0 0 2 2 0 0 | * * * * * * * * * 2 * * | 0 0 1 0 0 1
.xo ... .xx&#x  0 4 2 | 0 0 0 0 2 2 4 0 1 | 0 0 0 0 0 0 0 0 1 2 0 2 0 | * * * * * * * * * * 2 * | 0 0 0 1 0 1
... .ox .xx&#x  0 2 4 | 0 0 0 0 0 1 4 2 2 | 0 0 0 0 0 0 0 0 0 0 2 2 1 | * * * * * * * * * * * 2 | 0 0 0 0 1 1
---------------+-------+-------------------+---------------------------+-------------------------+------------
xx. xo. ox.&#x  4 4 0 | 2 2 8 0 2 2 0 0 0 | 1 4 4 4 0 0 0 0 1 0 0 0 0 | 2 2 2 0 0 0 0 0 0 0 0 0 | 1 * * * * *
x.o x.x o.x&#x  4 0 4 | 2 2 0 8 0 0 0 2 2 | 1 0 0 0 4 4 4 0 0 0 0 0 1 | 0 0 0 2 2 2 0 0 0 0 0 0 | * 1 * * * *
xxo xox ...&#x  4 2 2 | 2 2 4 4 1 0 4 1 0 | 1 2 2 0 2 2 0 4 0 2 2 0 0 | 1 0 0 1 0 0 2 2 0 1 0 0 | * * 2 * * *
xxo ... oxx&#x  2 4 2 | 1 0 4 4 2 2 4 0 1 | 0 2 0 2 2 0 2 4 1 2 0 2 0 | 0 1 0 0 1 0 2 0 2 0 1 0 | * * * 2 * *
... xox oxx&#x  2 2 4 | 0 1 4 4 0 1 4 2 2 | 0 0 2 2 0 2 2 4 0 0 2 2 1 | 0 0 1 0 0 1 0 2 2 0 0 1 | * * * * 2 *
.xo .ox .xx&#x  0 4 4 | 0 0 0 0 2 2 8 2 2 | 0 0 0 0 0 0 0 0 1 4 4 4 1 | 0 0 0 0 0 0 0 0 0 2 2 2 | * * * * * 1
or
o..2o..2o..    & | 12 |  2  4 | 1  4  6 2 |  6 2  5 | 2 3
-----------------+----+-------+-----------+---------+----
x.. ... ...    & |  2 | 12  * | 1  2  2 0 |  3 1  2 | 2 3
oo.2oo.2oo.&#x & |  2 |  * 24 | 0  1  2 1 |  3 1  3 | 1 3
-----------------+----+-------+-----------+---------+----
x.. x.. ...    & |  4 |  4  0 | 3  *  * * |  4 0  0 | 2 2
xx. ... ...&#x & |  4 |  2  2 | * 12  * * |  2 0  1 | 1 2
... xo. ...&#x & |  3 |  1  2 | *  * 24 * |  1 1  1 | 1 2
ooo2ooo2ooo&#x   |  3 |  0  3 | *  *  * 8 |  0 0  3 | 0 3
-----------------+----+-------+-----------+---------+----
xx. xo. ...&#x &   6 |  3  6 | 1  2  2 0 | 12 *  * | 1 1
... xo. ox.&#x &   4 |  2  4 | 0  0  4 0 |  * 6  * | 1 1
xxo ... ...&#x &   5 |  2  6 | 0  1  2 2 |  * * 12 | 0 2
-----------------+----+-------+-----------+---------+----
xx. xo. ox.&#x &   8 |  8  8 | 2  4  8 0 |  4 2  0 | 3 *
xxo xox ...&#x &   6 |  6 12 | 1  4  8 4 |  2 1  4 | * 6

x..2x..2o.. || .xo2.ox2.xx&#x   → height = sqrt(3/8) = 0.612372
({4} || ortho tepe)

o..2o..2o..      | 4 * | 2  4 0 0 0 | 1 4 4 2 2 0 0 0 | 4 2 2 4 1 0 0 | 2 2 2 0
.o.2.o.2.o.    & | * 8 | 0  2 1 1 2 | 0 2 1 2 2 1 3 2 | 1 2 1 3 2 1 3 | 1 1 3 1
-----------------+-----+------------+-----------------+---------------+--------
x.. ... ...    & | 2 0 | 4  * * * * | 1 2 2 0 0 0 0 0 | 4 1 1 2 0 0 0 | 2 2 1 0
oo.2oo.2oo.&#x & | 1 1 | * 16 * * * | 0 1 1 1 1 0 0 0 | 1 1 1 2 1 0 0 | 1 1 2 0
.x. ... ...    & | 0 2 | *  * 4 * * | 0 2 0 0 0 1 2 0 | 1 2 0 2 0 1 2 | 1 1 2 1
... ... .x.    & | 0 2 | *  * * 4 * | 0 0 0 2 0 1 0 2 | 0 2 1 0 2 0 3 | 1 0 3 1
.oo2.oo2.oo&#x   | 0 2 | *  * * * 8 | 0 0 0 0 1 0 2 1 | 0 0 0 2 1 1 2 | 0 1 2 1
-----------------+-----+------------+-----------------+---------------+--------
x.. x.. ...      | 4 0 | 4  0 0 0 0 | 1 * * * * * * * | 4 0 0 0 0 0 0 | 2 2 0 0
xx. ... ...&#x & | 2 2 | 1  2 1 0 0 | * 8 * * * * * * | 1 1 0 1 0 0 0 | 1 1 1 0
... xo. ...&#x & | 2 1 | 1  2 0 0 0 | * * 8 * * * * * | 1 0 1 1 0 0 0 | 1 1 1 0
... ... ox.&#x & | 1 2 | 0  2 0 1 0 | * * * 8 * * * * | 0 1 1 0 1 0 0 | 1 0 2 0
ooo2ooo2ooo&#x   | 1 2 | 0  2 0 0 1 | * * * * 8 * * * | 0 0 0 2 1 0 0 | 0 1 2 0
.x. ... .x.    & | 0 4 | 0  0 2 2 0 | * * * * * 2 * * | 0 2 0 0 0 0 2 | 1 0 2 1
.xo ... ...&#x & | 0 3 | 0  0 1 0 2 | * * * * * * 8 * | 0 0 0 1 0 1 1 | 0 1 1 1
... ... .xx&#x   | 0 4 | 0  0 0 2 2 | * * * * * * * 4 | 0 0 0 0 1 0 2 | 0 0 2 1
-----------------+-----+------------+-----------------+---------------+--------
xx. xo. ...&#x &  4 2 | 4  4 1 0 0 | 1 2 2 0 0 0 0 0 | 4 * * * * * * | 1 1 0 0
xx. ... ox.&#x &  2 4 | 1  4 2 2 0 | 0 2 0 2 0 1 0 0 | * 4 * * * * * | 1 0 1 0
... xo. ox.&#x &  2 2 | 1  4 0 1 0 | 0 0 2 2 0 0 0 0 | * * 4 * * * * | 1 0 1 0
xxo ... ...&#x &  2 3 | 1  4 1 0 2 | 0 1 1 0 2 0 1 0 | * * * 8 * * * | 0 1 1 0
... ... oxx&#x    1 4 | 0  4 0 2 2 | 0 0 0 2 2 0 0 1 | * * * * 4 * * | 0 0 2 0
.xo .ox ...&#x    0 4 | 0  0 2 0 4 | 0 0 0 0 0 0 4 0 | * * * * * 2 * | 0 1 0 1
.xo ... .xx&#x &  0 6 | 0  0 2 3 4 | 0 0 0 0 0 1 2 2 | * * * * * * 4 | 0 0 1 1
-----------------+-----+------------+-----------------+---------------+--------
xx. xo. ox.&#x &  4 4 | 4  8 2 2 0 | 1 4 4 4 0 1 0 0 | 2 2 2 0 0 0 0 | 2 * * *
xxo xox ...&#x    4 4 | 4  8 2 0 4 | 1 4 4 0 4 0 4 0 | 2 0 0 4 0 1 0 | * 2 * *
xxo ... oxx&#x &  2 6 | 1  8 2 3 4 | 0 2 2 4 4 1 2 2 | 0 1 1 2 2 0 1 | * * 4 *
.xo .ox .xx&#x    0 8 | 0  0 4 4 8 | 0 0 0 0 0 2 8 4 | 0 0 0 0 0 2 4 | * * * 1

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