Acronym tratoe
Name triangle truncated-octahedron duoprism
Circumradius sqrt(17/6) = 1.683251
Confer
more general:
n,toe-dip  
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

x3o x3x4o

. . . . . | 72 |  2  1  2 |  1  2  4  2  1 |  1  2  4  2 1 | 2 1 2
----------+----+----------+----------------+---------------+------
x . . . . |  2 | 72  *  * |  1  1  2  0  0 |  1  2  2  1 0 | 2 1 1
. . x . . |  2 |  * 36  * |  0  2  0  2  0 |  1  0  4  0 1 | 2 0 2
. . . x . |  2 |  *  * 72 |  0  0  2  1  1 |  0  1  2  2 1 | 1 1 2
----------+----+----------+----------------+---------------+------
x3o . . . |  3 |  3  0  0 | 24  *  *  *  * |  1  2  0  0 0 | 2 1 0
x . x . . |  4 |  2  2  0 |  * 36  *  *  * |  1  0  2  0 0 | 2 0 1
x . . x . |  4 |  2  0  2 |  *  * 72  *  * |  0  1  1  1 0 | 1 1 1
. . x3x . |  6 |  0  3  3 |  *  *  * 24  * |  0  0  2  0 1 | 1 0 2
. . . x4o |  4 |  0  0  4 |  *  *  *  * 18 |  0  0  0  2 1 | 0 1 2
----------+----+----------+----------------+---------------+------
x3o x . .   6 |  6  3  0 |  2  3  0  0  0 | 12  *  *  * * | 2 0 0
x3o . x .   6 |  6  0  3 |  2  0  3  0  0 |  * 24  *  * * | 1 1 0
x . x3x .  12 |  6  6  6 |  0  3  3  2  0 |  *  * 24  * * | 1 0 1
x . . x4o   8 |  4  0  8 |  0  0  4  0  2 |  *  *  * 18 * | 0 1 1
. . x3x4o  24 |  0 12 24 |  0  0  0  8  6 |  *  *  *  * 3 | 0 0 2
----------+----+----------+----------------+---------------+------
x3o x3x .  18 | 18  9  9 |  6  9  9  3  0 |  3  3  3  0 0 | 8 * *
x3o . x4o  12 | 12  0 12 |  4  0 12  0  3 |  0  4  0  3 0 | * 6 *
x . x3x4o  48 | 24 24 48 |  0 12 24 16 12 |  0  0  8  6 2 | * * 3

x3o x3x3x

. . . . . | 72 |  2  1  1  1 |  1  2  2  2  1  1  1 |  1  1  1  2  2  2 1 | 1 1 1 2
----------+----+-------------+----------------------+---------------------+--------
x . . . . |  2 | 72  *  *  * |  1  1  1  1  0  0  0 |  1  1  1  1  1  1 0 | 1 1 1 1
. . x . . |  2 |  * 36  *  * |  0  2  0  0  1  1  0 |  1  0  0  2  2  0 1 | 1 1 0 2
. . . x . |  2 |  *  * 36  * |  0  0  2  0  1  0  1 |  0  1  0  2  0  2 1 | 1 0 1 2
. . . . x |  2 |  *  *  * 36 |  0  0  0  2  0  1  1 |  0  0  1  0  2  2 1 | 0 1 1 2
----------+----+-------------+----------------------+---------------------+--------
x3o . . . |  3 |  3  0  0  0 | 24  *  *  *  *  *  * |  1  1  1  0  0  0 0 | 1 1 1 0
x . x . . |  4 |  2  2  0  0 |  * 36  *  *  *  *  * |  1  0  0  1  1  0 0 | 1 1 0 1
x . . x . |  4 |  2  0  2  0 |  *  * 36  *  *  *  * |  0  1  0  1  0  1 0 | 1 0 1 1
x . . . x |  4 |  2  0  0  2 |  *  *  * 36  *  *  * |  0  0  1  0  1  1 0 | 0 1 1 1
. . x3x . |  6 |  0  3  3  0 |  *  *  *  * 12  *  * |  0  0  0  2  0  0 1 | 1 0 0 2
. . x . x |  4 |  0  2  0  2 |  *  *  *  *  * 18  * |  0  0  0  0  2  0 1 | 0 1 0 2
. . . x3x |  6 |  0  0  3  3 |  *  *  *  *  *  * 12 |  0  0  0  0  0  2 1 | 0 0 1 2
----------+----+-------------+----------------------+---------------------+--------
x3o x . .   6 |  6  3  0  0 |  2  3  0  0  0  0  0 | 12  *  *  *  *  * * | 1 1 0 0
x3o . x .   6 |  6  0  3  0 |  2  0  3  0  0  0  0 |  * 12  *  *  *  * * | 1 0 1 0
x3o . . x   6 |  6  0  0  3 |  2  0  0  3  0  0  0 |  *  * 12  *  *  * * | 0 1 1 0
x . x3x .  12 |  6  6  6  0 |  0  3  3  0  2  0  0 |  *  *  * 12  *  * * | 1 0 0 1
x . x . x   8 |  4  4  0  4 |  0  2  0  2  0  2  0 |  *  *  *  * 18  * * | 0 1 0 1
x . . x3x  12 |  6  0  6  6 |  0  0  3  3  0  0  2 |  *  *  *  *  * 12 * | 0 0 1 1
. . x3x3x  24 |  0 12 12 12 |  0  0  0  0  4  6  4 |  *  *  *  *  *  * 3 | 0 0 0 2
----------+----+-------------+----------------------+---------------------+--------
x3o x3x .  18 | 18  9  9  0 |  6  9  9  0  3  0  0 |  3  3  0  3  0  0 0 | 4 * * *
x3o x . x  12 | 12  6  0  6 |  4  6  0  6  0  3  0 |  2  0  2  0  3  0 0 | * 6 * *
x3o . x3x  18 | 18  0  9  9 |  6  0  9  9  0  0  3 |  0  3  3  0  0  3 0 | * * 4 *
x . x3x3x  48 | 24 24 24 24 |  0 12 12 12  8 12  8 |  0  0  0  4  6  4 2 | * * * 3

xxx3xxx3xxx&#x   → all pairwse heights = 1

o..3o..3o..    | 24  *  * |  1  1  1  1  1  0  0  0  0  0  0  0 | 1 1 1  1  1  1  1  1  1  1 0 0 0  0  0  0 0 0 0 | 1 1 1 1 1 1 1  1  1  1 0 0 0 0 0 | 1 1 1 1 1 0
.o.3.o.3.o.    |  * 24  * |  0  0  0  1  0  1  1  1  1  0  0  0 | 0 0 0  1  1  1  0  0  0  1 1 1 1  1  1  1 0 0 0 | 0 1 1 1 0 0 0  1  1  1 1 1 1 1 0 | 1 0 1 1 1 1
..o3..o3..o    |  *  * 24 |  0  0  0  0  1  0  0  0  1  1  1  1 | 0 0 0  0  0  0  1  1  1  1 0 0 0  1  1  1 1 1 1 | 0 0 0 0 1 1 1  1  1  1 0 1 1 1 1 | 0 1 1 1 1 1
---------------+----------+-------------------------------------+-------------------------------------------------+----------------------------------+------------
x.. ... ...    |  2  0  0 | 12  *  *  *  *  *  *  *  *  *  *  * | 1 1 0  1  0  0  1  0  0  0 0 0 0  0  0  0 0 0 0 | 1 1 1 0 1 1 0  1  0  0 0 0 0 0 0 | 1 1 1 1 0 0
... x.. ...    |  2  0  0 |  * 12  *  *  *  *  *  *  *  *  *  * | 1 0 1  0  1  0  0  1  0  0 0 0 0  0  0  0 0 0 0 | 1 1 0 1 1 0 1  0  1  0 0 0 0 0 0 | 1 1 1 0 1 0
... ... x..    |  2  0  0 |  *  * 12  *  *  *  *  *  *  *  *  * | 0 1 1  0  0  1  0  0  1  0 0 0 0  0  0  0 0 0 0 | 1 0 1 1 0 1 1  0  0  1 0 0 0 0 0 | 1 1 0 1 1 0
oo.3oo.3oo.&#x |  1  1  0 |  *  *  * 24  *  *  *  *  *  *  *  * | 0 0 0  1  1  1  0  0  0  1 0 0 0  0  0  0 0 0 0 | 0 1 1 1 0 0 0  1  1  1 0 0 0 0 0 | 1 0 1 1 1 0
o.o3o.o3o.o&#x |  1  0  1 |  *  *  *  * 24  *  *  *  *  *  *  * | 0 0 0  0  0  0  1  1  1  1 0 0 0  0  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 |  *  *  *  *  * 12  *  *  *  *  *  * | 0 0 0  1  0  0  0  0  0  0 1 1 0  1  0  0 0 0 0 | 0 1 1 0 0 0 0  1  0  0 1 1 1 0 0 | 1 0 1 1 0 1
... .x. ...    |  0  2  0 |  *  *  *  *  *  * 12  *  *  *  *  * | 0 0 0  0  1  0  0  0  0  0 1 0 1  0  1  0 0 0 0 | 0 1 0 1 0 0 0  0  1  0 1 1 0 1 0 | 1 0 1 0 1 1
... ... .x.    |  0  2  0 |  *  *  *  *  *  *  * 12  *  *  *  * | 0 0 0  0  0  1  0  0  0  0 0 1 1  0  0  1 0 0 0 | 0 0 1 1 0 0 0  0  0  1 1 0 1 1 0 | 1 0 0 1 1 1
.oo3.oo3.oo&#x |  0  1  1 |  *  *  *  *  *  *  *  * 24  *  *  * | 0 0 0  0  0  0  0  0  0  1 0 0 0  1  1  1 0 0 0 | 0 0 0 0 0 0 0  1  1  1 0 1 1 1 0 | 0 0 1 1 1 1
..x ... ...    |  0  0  2 |  *  *  *  *  *  *  *  *  * 12  *  * | 0 0 0  0  0  0  1  0  0  0 0 0 0  1  0  0 1 1 0 | 0 0 0 0 1 1 0  1  0  0 0 1 1 0 1 | 0 1 1 1 0 1
... ..x ...    |  0  0  2 |  *  *  *  *  *  *  *  *  *  * 12  * | 0 0 0  0  0  0  0  1  0  0 0 0 0  0  1  0 1 0 1 | 0 0 0 0 1 0 1  0  1  0 0 1 0 1 1 | 0 1 1 0 1 1
... ... ..x    |  0  0  2 |  *  *  *  *  *  *  *  *  *  *  * 12 | 0 0 0  0  0  0  0  0  1  0 0 0 0  0  0  1 0 1 1 | 0 0 0 0 0 1 1  0  0  1 0 0 1 1 1 | 0 1 0 1 1 1
---------------+----------+-------------------------------------+-------------------------------------------------+----------------------------------+------------
x..3x.. ...    |  6  0  0 |  3  3  0  0  0  0  0  0  0  0  0  0 | 4 * *  *  *  *  *  *  *  * * * *  *  *  * * * * | 1 1 0 0 1 0 0  0  0  0 0 0 0 0 0 | 1 1 1 0 0 0
x.. ... x..    |  4  0  0 |  2  0  2  0  0  0  0  0  0  0  0  0 | * 6 *  *  *  *  *  *  *  * * * *  *  *  * * * * | 1 0 1 0 0 1 0  0  0  0 0 0 0 0 0 | 1 1 0 1 0 0
... x..3x..    |  6  0  0 |  0  3  3  0  0  0  0  0  0  0  0  0 | * * 4  *  *  *  *  *  *  * * * *  *  *  * * * * | 1 0 0 1 0 0 1  0  0  0 0 0 0 0 0 | 1 1 0 0 1 0
xx. ... ...&#x |  2  2  0 |  1  0  0  2  0  1  0  0  0  0  0  0 | * * * 12  *  *  *  *  *  * * * *  *  *  * * * * | 0 1 1 0 0 0 0  1  0  0 0 0 0 0 0 | 1 0 1 1 0 0 
... xx. ...&#x |  2  2  0 |  0  1  0  2  0  0  1  0  0  0  0  0 | * * *  * 12  *  *  *  *  * * * *  *  *  * * * * | 0 1 0 1 0 0 0  0  1  0 0 0 0 0 0 | 1 0 1 0 1 0
... ... xx.&#x |  2  2  0 |  0  0  1  2  0  0  0  1  0  0  0  0 | * * *  *  * 12  *  *  *  * * * *  *  *  * * * * | 0 0 1 1 0 0 0  0  0  1 0 0 0 0 0 | 1 0 0 1 1 0
x.x ... ...&#x |  2  0  2 |  1  0  0  0  2  0  0  0  0  1  0  0 | * * *  *  *  * 12  *  *  * * * *  *  *  * * * * | 0 0 0 0 1 1 0  1  0  0 0 0 0 0 0 | 0 1 1 1 0 0
... x.x ...&#x |  2  0  2 |  0  1  0  0  2  0  0  0  0  0  1  0 | * * *  *  *  *  * 12  *  * * * *  *  *  * * * * | 0 0 0 0 1 0 1  0  1  0 0 0 0 0 0 | 0 1 1 0 1 0
... ... x.x&#x |  2  0  2 |  0  0  1  0  2  0  0  0  0  0  0  1 | * * *  *  *  *  *  * 12  * * * *  *  *  * * * * | 0 0 0 0 0 1 1  0  0  1 0 0 0 0 0 | 0 1 0 1 1 0
ooo3ooo3ooo&#x |  1  1  1 |  0  0  0  1  1  0  0  0  1  0  0  0 | * * *  *  *  *  *  *  * 24 * * *  *  *  * * * * | 0 0 0 0 0 0 0  1  1  1 0 0 0 0 0 | 0 0 1 1 1 0
.x.3.x. ...    |  0  6  0 |  0  0  0  0  0  3  3  0  0  0  0  0 | * * *  *  *  *  *  *  *  * 4 * *  *  *  * * * * | 0 1 0 0 0 0 0  0  0  0 1 1 0 0 0 | 1 0 1 0 0 1
.x. ... .x.    |  0  4  0 |  0  0  0  0  0  2  0  2  0  0  0  0 | * * *  *  *  *  *  *  *  * * 6 *  *  *  * * * * | 0 0 1 0 0 0 0  0  0  0 1 0 1 0 0 | 1 0 0 1 0 1
... .x.3.x.    |  0  6  0 |  0  0  0  0  0  0  3  3  0  0  0  0 | * * *  *  *  *  *  *  *  * * * 4  *  *  * * * * | 0 0 0 1 0 0 0  0  0  0 1 0 0 1 0 | 1 0 0 0 1 1
.xx ... ...&#x |  0  2  2 |  0  0  0  0  0  1  0  0  2  1  0  0 | * * *  *  *  *  *  *  *  * * * * 12  *  * * * * | 0 0 0 0 0 0 0  1  0  0 0 1 1 0 0 | 0 0 1 1 0 1
... .xx ...&#x |  0  2  2 |  0  0  0  0  0  0  1  0  2  0  1  0 | * * *  *  *  *  *  *  *  * * * *  * 12  * * * * | 0 0 0 0 0 0 0  0  1  0 0 1 0 1 0 | 0 0 1 0 1 1
... ... .xx&#x |  0  2  2 |  0  0  0  0  0  0  0  1  2  0  0  1 | * * *  *  *  *  *  *  *  * * * *  *  * 12 * * * | 0 0 0 0 0 0 0  0  0  1 0 0 1 1 0 | 0 0 0 1 1 1
..x3..x ...    |  0  0  6 |  0  0  0  0  0  0  0  0  0  3  3  0 | * * *  *  *  *  *  *  *  * * * *  *  *  * 4 * * | 0 0 0 0 1 0 0  0  0  0 0 1 0 0 1 | 0 1 1 0 0 1
..x ... ..x    |  0  0  4 |  0  0  0  0  0  0  0  0  0  2  0  2 | * * *  *  *  *  *  *  *  * * * *  *  *  * * 6 * | 0 0 0 0 0 1 0  0  0  0 0 0 1 0 1 | 0 1 0 1 0 1
... ..x3..x    |  0  0  6 |  0  0  0  0  0  0  0  0  0  0  3  3 | * * *  *  *  *  *  *  *  * * * *  *  *  * * * 4 | 0 0 0 0 0 0 1  0  0  0 0 0 0 1 1 | 0 1 0 0 1 1
---------------+----------+-------------------------------------+-------------------------------------------------+----------------------------------+------------
x..3x..3x..     24  0  0 | 12 12 12  0  0  0  0  0  0  0  0  0 | 4 6 4  0  0  0  0  0  0  0 0 0 0  0  0  0 0 0 0 | 1 * * * * * *  *  *  * * * * * * | 1 1 0 0 0 0
xx.3xx. ...&#x   6  6  0 |  3  3  0  6  0  3  3  0  0  0  0  0 | 1 0 0  3  3  0  0  0  0  0 1 0 0  0  0  0 0 0 0 | * 4 * * * * *  *  *  * * * * * * | 1 0 1 0 0 0
xx. ... xx.&#x   4  4  0 |  2  0  2  4  0  2  0  2  0  0  0  0 | 0 1 0  2  0  2  0  0  0  0 0 1 0  0  0  0 0 0 0 | * * 6 * * * *  *  *  * * * * * * | 1 0 0 1 0 0
... xx.3xx.&#x   6  6  0 |  0  3  3  6  0  0  3  3  0  0  0  0 | 0 0 1  0  3  3  0  0  0  0 0 0 1  0  0  0 0 0 0 | * * * 4 * * *  *  *  * * * * * * | 1 0 0 0 1 0
x.x3x.x ...&#x   6  0  6 |  3  3  0  0  6  0  0  0  0  3  3  0 | 1 0 0  0  0  0  3  3  0  0 0 0 0  0  0  0 1 0 0 | * * * * 4 * *  *  *  * * * * * * | 0 1 1 0 0 0
x.x ... x.x&#x   4  0  4 |  2  0  2  0  4  0  0  0  0  2  0  2 | 0 1 0  0  0  0  2  0  2  0 0 0 0  0  0  0 0 1 0 | * * * * * 6 *  *  *  * * * * * * | 0 1 0 1 0 0
... x.x3x.x&#x   6  0  6 |  0  3  3  0  6  0  0  0  0  0  3  3 | 0 0 1  0  0  0  0  3  3  0 0 0 0  0  0  0 0 0 1 | * * * * * * 4  *  *  * * * * * * | 0 1 0 0 1 0
xxx ... ...&#x   2  2  2 |  1  0  0  2  2  1  0  0  2  1  0  0 | 0 0 0  1  0  0  1  0  0  2 0 0 0  1  0  0 0 0 0 | * * * * * * * 12  *  * * * * * * | 0 0 1 1 0 0
... xxx ...&#x   2  2  2 |  0  1  0  2  2  0  1  0  2  0  1  0 | 0 0 0  0  1  0  0  1  0  2 0 0 0  0  1  0 0 0 0 | * * * * * * *  * 12  * * * * * * | 0 0 1 0 1 0
... ... xxx&#x   2  2  2 |  0  0  1  2  2  0  0  1  2  0  0  1 | 0 0 0  0  0  1  0  0  1  2 0 0 0  0  0  1 0 0 0 | * * * * * * *  *  * 12 * * * * * | 0 0 0 1 1 0
.x.3.x.3.x.      0 24  0 |  0  0  0  0  0 12 12 12  0  0  0  0 | 0 0 0  0  0  0  0  0  0  0 4 6 4  0  0  0 0 0 0 | * * * * * * *  *  *  * 1 * * * * | 1 0 0 0 0 1
.xx3.xx ...&#x   0  6  6 |  0  0  0  0  0  3  3  0  6  3  3  0 | 0 0 0  0  0  0  0  0  0  0 1 0 0  3  3  0 1 0 0 | * * * * * * *  *  *  * * 4 * * * | 0 0 1 0 0 1
.xx ... .xx&#x   0  4  4 |  0  0  0  0  0  2  0  2  4  2  0  2 | 0 0 0  0  0  0  0  0  0  0 0 1 0  2  0  2 0 1 0 | * * * * * * *  *  *  * * * 6 * * | 0 0 0 1 0 1
... .xx3.xx&#x   0  6  6 |  0  0  0  0  0  0  3  3  6  0  3  3 | 0 0 0  0  0  0  0  0  0  0 0 0 1  0  3  3 0 0 1 | * * * * * * *  *  *  * * * * 4 * | 0 0 0 0 1 1
..x3..x3..x      0  0 24 |  0  0  0  0  0  0  0  0  0 12 12 12 | 0 0 0  0  0  0  0  0  0  0 0 0 0  0  0  0 4 6 4 | * * * * * * *  *  *  * * * * * 1 | 0 1 0 0 0 1
---------------+----------+-------------------------------------+-------------------------------------------------+----------------------------------+------------
xx.3xx.3xx.&#x  24 24  0 | 12 12 12 24  0 12 12 12  0  0  0  0 | 4 6 4 12 12 12  0  0  0  0 4 6 4  0  0  0 0 0 0 | 1 4 6 4 0 0 0  0  0  0 1 0 0 0 0 | 1 * * * * *
x.x3x.x3x.x&#x  24  0 24 | 12 12 12  0 24  0  0  0  0 12 12 12 | 4 6 4  0  0  0 12 12 12  0 0 0 0  0  0  0 4 6 4 | 1 0 0 0 4 6 4  0  0  0 0 0 0 0 1 | * 1 * * * *
xxx3xxx ...&#x   6  6  6 |  3  3  0  6  6  3  3  0  6  3  3  0 | 1 0 0  3  3  0  3  3  0  6 1 0 0  3  3  0 1 0 0 | 0 1 0 0 1 0 0  3  3  0 0 1 0 0 0 | * * 4 * * *
xxx ... xxx&#x   4  4  4 |  2  0  2  4  4  2  0  2  4  2  0  2 | 0 1 0  2  0  2  2  0  2  4 0 1 0  2  0  2 0 1 0 | 0 0 1 0 0 1 0  2  0  2 0 0 1 0 0 | * * * 6 * *
... xxx3xxx&#x   6  6  6 |  0  3  3  6  6  0  3  3  6  0  3  3 | 0 0 1  0  3  3  0  3  3  6 0 0 1  0  3  3 0 0 1 | 0 0 0 1 0 0 1  0  3  3 0 0 0 1 0 | * * * * 4 *
.xx3.xx3.xx&#x   0 24 24 |  0  0  0  0  0 12 12 12 24 12 12 12 | 0 0 0  0  0  0  0  0  0  0 4 6 4 12 12 12 4 6 4 | 0 0 0 0 0 0 0  0  0  0 1 4 6 4 1 | * * * * * 1

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