Acronym trahix
Name triangle - hexateron duoprism,
vertex figure of brene
Circumradius sqrt(3)/2 = 0.866025
Confer n,hix-dip  

Incidence matrix according to Dynkin symbol

x3o x3o3o3o3o

. . . . . . . | 18 |  2  5 | 1 10 10 |  5 20 10 | 10 10  5 | 10 10 1 | 5 2
--------------+----+-------+---------+----------+----------+---------+----
x . . . . . . |  2 | 18  * | 1  5  0 |  5 10  0 | 10  5  0 | 10  5 0 | 5 1
. . x . . . . |  2 |  * 45 | 0  2  4 |  1  8  6 |  4 12  4 |  6  8 1 | 4 2
--------------+----+-------+---------+----------+----------+---------+----
x3o . . . . . |  3 |  3  0 | 6  *  *   5  0  0 | 10  0  0 | 10  0 0 | 5 0
x . x . . . . |  4 |  2  2 | * 45  * |  1  4  0 |  4  6  0 |  6  4 0 | 4 1
. . x3o . . . |  3 |  0  3 | *  * 60 |  0  2  3 |  1  6  3 |  3  6 1 | 3 2
--------------+----+-------+---------+----------+----------+---------+----
x3o x . . . .   6 |  6  3 | 2  3  0 | 15  *  *   4  0  0 |  6  0 0 | 4 0
x . x3o . . .   6 |  3  6 | 0  3  2 |  * 60  * |  1  3  0 |  3  3 0 | 3 1
. . x3o3o . .   4 |  0  6 | 0  0  4 |  *  * 45 |  0  2  2 |  1  4 1 | 2 2
--------------+----+-------+---------+----------+----------+---------+----
x3o x3o . . .   9 |  9  9 | 3  9  3 |  3  3  0 | 20  *  * |  3  0 0 | 3 0
x . x3o3o . .   8 |  4 12 | 0  6  8 |  0  4  2 |  * 45  * |  1  2 0 | 2 1
. . x3o3o3o .   5 |  0 10 | 0  0 10 |  0  0  5 |  *  * 18 |  0  2 1 | 1 2
--------------+----+-------+---------+----------+----------+---------+----
x3o x3o3o . .  12 | 12 18 | 4 18 12 |  6 12  3 |  4  3  0 | 15  * * | 2 0
x . x3o3o3o .  10 |  5 20 | 0 10 20 |  0 10 10 |  0  5  2 |  * 18 * | 1 1
. . x3o3o3o3o   6 |  0 15 | 0  0 20 |  0  0 15 |  0  0  6 |  *  * 3 | 0 2
--------------+----+-------+---------+----------+----------+---------+----
x3o x3o3o3o .  15 | 15 30 | 5 30 30 | 10 30 15 | 10 15  3 |  5  3 0 | 6 *
x . x3o3o3o3o  12 |  6 30 | 0 15 40 |  0 20 30 |  0 15 12 |  0  6 2 | * 3

ox xx3oo3oo3oo3oo&#x   → height = sqrt(3)/2 = 0.866025
(hix || hixip)

o. o.3o.3o.3o.3o.    | 6  * |  5  2 0  0 | 10 1 10  0  0 | 10  5 20  0  0 | 5 10 20  0  0 | 1 10 10 0 0 | 5 2 0
.o .o3.o3.o3.o3.o    | * 12 |  0  1 1  5 |  0 1  5  5 10 |  0  5 10 10 10 | 0 10 10 10  5 | 0 10  5 5 1 | 5 1 1
---------------------+------+------------+---------------+----------------+---------------+-------------+------
.. x. .. .. .. ..    | 2  0 | 15  * *  * |  4 0  2  0  0 |  6  1  8  0  0 | 4  4 12  0  0 | 1  6  8 0 0 | 4 2 0
oo oo3oo3oo3oo3oo&#x | 1  1 |  * 12 *  * |  0 1  5  0  0 |  0  5 10  0  0 | 0 10 10  0  0 | 0 10  5 0 0 | 5 1 0
.x .. .. .. .. ..    | 0  2 |  *  * 6  * |  0 1  0  5  0 |  0  5  0 10  0 | 0 10  0 10  0 | 0 10  0 5 0 | 5 0 1
.. .x .. .. .. ..    | 0  2 |  *  * * 30 |  0 0  1  1  4 |  0  1  4  4  6 | 0  4  6  6  4 | 0  6  4 4 1 | 4 1 1
---------------------+------+------------+---------------+----------------+---------------+-------------+------
.. x.3o. .. .. ..    | 3  0 |  3  0 0  0 | 20 *  *  *  * |  3  0  2  0  0 | 3  1  6  0  0 | 1  3  6 0 0 | 3 2 0
ox .. .. .. .. ..&#x | 1  2 |  0  2 1  0 |  * 6  *  *  *   0  5  0  0  0 | 0 10  0  0  0 | 0 10  0 0 0 | 5 0 0
.. xx .. .. .. ..&#x | 2  2 |  1  2 0  1 |  * * 30  *  * |  0  1  4  0  0 | 0  4  6  0  0 | 0  6  4 0 0 | 4 1 0
.x .x .. .. .. ..    | 0  4 |  0  0 2  2 |  * *  * 15  * |  0  1  0  4  0 | 0  4  0  6  0 | 0  6  0 4 0 | 4 0 1
.. .x3.o .. .. ..    | 0  3 |  0  0 0  3 |  * *  *  * 40 |  0  0  1  1  3 | 0  1  3  3  3 | 0  3  3 3 1 | 3 1 1
---------------------+------+------------+---------------+----------------+---------------+-------------+------
.. x.3o.3o. .. ..     4  0 |  6  0 0  0 |  4 0  0  0  0 | 15  *  *  *  * | 2  0  2  0  0 | 1  1  4 0 0 | 2 2 0
ox xx .. .. .. ..&#x  2  4 |  1  4 2  2 |  0 2  2  1  0 |  * 15  *  *  *  0  4  0  0  0 | 0  6  0 0 0 | 4 0 0
.. xx3oo .. .. ..&#x  3  3 |  3  3 0  3 |  1 0  3  0  1 |  *  * 40  *  * | 0  1  3  0  0 | 0  3  3 0 0 | 3 1 0
.x .x3.o .. .. ..     0  6 |  0  0 3  6 |  0 0  0  3  2 |  *  *  * 20  * | 0  1  0  3  0 | 0  3  0 3 0 | 3 0 1
.. .x3.o3.o .. ..     0  4 |  0  0 0  6 |  0 0  0  0  4 |  *  *  *  * 30 | 0  0  1  1  2 | 0  1  2 2 1 | 2 1 1
---------------------+------+------------+---------------+----------------+---------------+-------------+------
.. x.3o.3o.3o. ..     5  0 | 10  0 0  0 | 10 0  0  0  0 |  5  0  0  0  0 | 6  *  *  *  * | 1  0  2 0 0 | 1 2 0
ox xx3oo .. .. ..&#x  3  6 |  3  6 3  6 |  1 3  6  3  2 |  0  3  2  1  0 | * 20  *  *  * | 0  3  0 0 0 | 3 0 0
.. xx3oo3oo .. ..&#x  4  4 |  6  4 0  6 |  4 0  6  0  4 |  1  0  4  0  1 | *  * 30  *  * | 0  1  2 0 0 | 2 1 0
.x .x3.o3.o .. ..     0  8 |  0  0 4 12 |  0 0  0  6  8 |  0  0  0  4  2 | *  *  * 15  * | 0  1  0 2 0 | 2 0 1
.. .x3.o3.o3.o ..     0  5 |  0  0 0 10 |  0 0  0  0 10 |  0  0  0  0  5 | *  *  *  * 12 | 0  0  1 1 1 | 1 1 1
---------------------+------+------------+---------------+----------------+---------------+-------------+------
.. x.3o.3o.3o.3o.     6  0 | 15  0 0  0 | 20 0  0  0  0 | 15  0  0  0  0 | 6  0  0  0  0 | 1  *  * * * | 0 2 0
ox xx3oo3oo .. ..&#x  4  8 |  6  8 4 12 |  4 4 12  6  8 |  1  6  8  4  2 | 0  4  2  1  0 | * 15  * * * | 2 0 0
.. xx3oo3oo3oo ..&#x  5  5 | 10  5 0 10 | 10 0 10  0 10 |  5  0 10  0  5 | 1  0  5  0  1 | *  * 12 * * | 1 1 0
.x .x3.o3.o3.o ..     0 10 |  0  0 5 20 |  0 0  0 10 20 |  0  0  0 10 10 | 0  0  0  5  2 | *  *  * 6 * | 1 0 1
.. .x3.o3.o3.o3.o     0  6 |  0  0 0 15 |  0 0  0  0 20 |  0  0  0  0 15 | 0  0  0  0  6 | *  *  * * 2 | 0 1 1
---------------------+------+------------+---------------+----------------+---------------+-------------+------
ox xx3oo3oo3oo ..&#x  5 10 | 10 10 5 20 | 10 5 20 10 20 |  5 10 20 10 10 | 1 10 10  5  2 | 0  5  2 1 0 | 6 * *
.. xx3oo3oo3oo3oo&#x  6  6 | 15  6 0 15 | 20 0 15  0 20 | 15  0 20  0 15 | 6  0 15  0  6 | 1  0  6 0 1 | * 2 *
.x .x3.o3.o3.o3.o     0 12 |  0  0 6 30 |  0 0  0 15 40 |  0  0  0 20 30 | 0  0  0 15 12 | 0  0  0 6 2 | * * 1

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