Acronym trahex
Name triangle - hexadecachoron duoprism,
vertex figure of barz
Circumradius sqrt(5/6) = 0.912871
Confer n,hex-dip  

Incidence matrix according to Dynkin symbol

x3o x3o3o4o

. . . . . . | 24 |  2  6 | 1 12 12 |  6 12  8 | 12 16 1 |  8 2
------------+----+-------+---------+----------+---------+-----
x . . . . . |  2 | 24  * | 1  6  0 |  6 12  0 | 12  8 0 |  8 1
. . x . . . |  2 |  * 72 | 0  2  4 |  1  8  4 |  4  8 1 |  4 2
------------+----+-------+---------+----------+---------+-----
x3o . . . . |  3 |  3  0 | 8  *  *   6  0  0 | 12  0 0 |  8 0
x . x . . . |  4 |  2  2 | * 72  * |  1  4  0 |  4  4 0 |  4 1
. . x3o . . |  3 |  0  3 | *  * 96 |  0  2  2 |  1  4 1 |  2 2
------------+----+-------+---------+----------+---------+-----
x3o x . . .   6 |  6  3 | 2  3  0 | 24  *  * |  4  0 0 |  4 0
x . x3o . .   6 |  3  6 | 0  3  2 |  * 96  * |  1  2 0 |  2 1
. . x3o3o .   4 |  0  6 | 0  0  4 |  *  * 48 |  0  2 1 |  1 2
------------+----+-------+---------+----------+---------+-----
x3o x3o . .   9 |  9  9 | 3  9  3 |  3  3  0 | 32  * * |  2 0
x . x3o3o .   8 |  4 12 | 0  6  8 |  0  4  2 |  * 48 * |  1 1
. . x3o3o4o   8 |  0 24 | 0  0 32 |  0  0 16 |  *  * 3 |  0 2
------------+----+-------+---------+----------+---------+-----
x3o x3o3o .  12 | 12 18 | 4 18 12 |  6 12  3 |  4  3 0 | 16 *
x . x3o3o4o  16 |  8 48 | 0 24 64 |  0 32 32 |  0 16 2 |  * 3

x3o x3o3o *d3o

. . . . .    . | 24 |  2  6 | 1 12 12 |  6 12  4  4 | 12  8  8 1 | 4 4 2
---------------+----+-------+---------+-------------+------------+------
x . . . .    . |  2 | 24  * | 1  6  0 |  6 12  0  0 | 12  4  4 0 | 4 4 1
. . x . .    . |  2 |  * 72 | 0  2  4 |  1  8  2  2 |  4  4  4 1 | 2 2 2
---------------+----+-------+---------+-------------+------------+------
x3o . . .    . |  3 |  3  0 | 8  *  *   6  0  0  0 | 12  0  0 0 | 4 4 0
x . x . .    . |  4 |  2  2 | * 72  * |  1  4  0  0 |  4  2  2 0 | 2 2 1
. . x3o .    . |  3 |  0  3 | *  * 96 |  0  2  1  1 |  1  2  2 1 | 1 1 2
---------------+----+-------+---------+-------------+------------+------
x3o x . .    .   6 |  6  3 | 2  3  0 | 24  *  *  * |  4  0  0 0 | 2 2 0
x . x3o .    .   6 |  3  6 | 0  3  2 |  * 96  *  * |  1  1  1 0 | 1 1 1
. . x3o3o    .   4 |  0  6 | 0  0  4 |  *  * 24  * |  0  2  0 1 | 1 0 2
. . x3o . *d3o   4 |  0  6 | 0  0  4 |  *  *  * 24 |  0  0  2 1 | 0 1 2
---------------+----+-------+---------+-------------+------------+------
x3o x3o .    .   9 |  9  9 | 3  9  3 |  3  3  0  0 | 32  *  * * | 1 1 0
x . x3o3o    .   8 |  4 12 | 0  6  8 |  0  4  2  0 |  * 24  * * | 1 0 1
x . x3o . *d3o   8 |  4 12 | 0  6  8 |  0  4  0  2 |  *  * 24 * | 0 1 1
. . x3o3o *d3o   8 |  0 24 | 0  0 32 |  0  0  8  8 |  *  *  * 3 | 0 0 2
---------------+----+-------+---------+-------------+------------+------
x3o x3o3o    .  12 | 12 18 | 4 18 12 |  6 12  3  0 |  4  3  0 0 | 8 * *
x3o x3o . *d3o  12 | 12 18 | 4 18 12 |  6 12  0  3 |  4  0  3 0 | * 8 *
x . x3o3o *d3o  16 |  8 48 | 0 24 64 |  0 32 16 16 |  0  8  8 2 | * * 3

ox xx3oo3oo4oo&#x   → height = 1/2
(hex || hexip)

o. o.3o.3o.4o.    | 8  * |  6  2 0  0 | 12 1 12  0  0 |  8  6 24  0  0 | 1 12 16  0 0 |  8 2 0
.o .o3.o3.o4.o    | * 16 |  0  1 1  6 |  0 1  6  6 12 |  0  6 12 12  8 | 0 12  8  8 1 |  8 1 1
------------------+------+------------+---------------+----------------+--------------+-------
.. x. .. .. ..    | 2  0 | 24  * *  * |  4 0  2  0  0 |  4  1  8  0  0 | 1  4  8  0 0 |  4 2 0
oo oo3oo3oo4oo&#x | 1  1 |  * 16 *  * |  0 1  6  0  0 |  0  6 12  0  0 | 0 12  8  0 0 |  8 1 0
.x .. .. .. ..    | 0  2 |  *  * 8  * |  0 1  0  6  0 |  0  6  0 12  0 | 0 12  0  8 0 |  8 0 1
.. .x .. .. ..    | 0  2 |  *  * * 48 |  0 0  1  1  4 |  0  1  4  4  4 | 0  4  4  4 1 |  4 1 1
------------------+------+------------+---------------+----------------+--------------+-------
.. x.3o. .. ..    | 3  0 |  3  0 0  0 | 32 *  *  *  * |  2  0  2  0  0 | 1  1  4  0 0 |  2 2 0
ox .. .. .. ..&#x | 1  2 |  0  2 1  0 |  * 8  *  *  *   0  6  0  0  0 | 0 12  0  0 0 |  8 0 0
.. xx .. .. ..&#x | 2  2 |  1  2 0  1 |  * * 48  *  * |  0  1  4  0  0 | 0  4  4  0 0 |  4 1 0
.x .x .. .. ..    | 0  4 |  0  0 2  2 |  * *  * 24  * |  0  1  0  4  0 | 0  4  0  4 0 |  4 0 1
.. .x3.o .. ..    | 0  3 |  0  0 0  3 |  * *  *  * 64 |  0  0  1  1  2 | 0  1  2  2 1 |  2 1 1
------------------+------+------------+---------------+----------------+--------------+-------
.. x.3o.3o. ..     4  0 |  6  0 0  0 |  4 0  0  0  0 | 16  *  *  *  * | 1  0  2  0 0 |  1 2 0
ox xx .. .. ..&#x  2  4 |  1  4 2  2 |  0 2  2  1  0 |  * 24  *  *  * | 0  4  0  0 0 |  4 0 0
.. xx3oo .. ..&#x  3  3 |  3  3 0  3 |  1 0  3  0  1 |  *  * 64  *  * | 0  1  2  0 0 |  2 1 0
.x .x3.o .. ..     0  6 |  0  0 3  6 |  0 0  0  3  2 |  *  *  * 32  * | 0  1  0  2 0 |  2 0 1
.. .x3.o3.o ..     0  4 |  0  0 0  6 |  0 0  0  0  4 |  *  *  *  * 32 | 0  0  1  1 1 |  1 1 1
------------------+------+------------+---------------+----------------+--------------+-------
.. x.3o.3o.4o.     8  0 | 24  0 0  0 | 32 0  0  0  0 | 16  0  0  0  0 | 1  *  *  * * |  0 2 0
ox xx3oo .. ..&#x  3  6 |  3  6 3  6 |  1 3  6  3  2 |  0  3  2  1  0 | * 32  *  * * |  2 0 0
.. xx3oo3oo ..&#x  4  4 |  6  4 0  6 |  4 0  6  0  4 |  1  0  4  0  1 | *  * 32  * * |  1 1 0
.x .x3.o3.o ..     0  8 |  0  0 4 12 |  0 0  0  6  8 |  0  0  0  4  2 | *  *  * 16 * |  1 0 1
.. .x3.o3.o4.o     0  8 |  0  0 0 24 |  0 0  0  0 32 |  0  0  0  0 16 | *  *  *  * 2 |  0 1 1
------------------+------+------------+---------------+----------------+--------------+-------
ox xx3oo3oo ..&#x  4  8 |  6  8 4 12 |  4 4 12  6  8 |  1  6  8  4  2 | 0  4  2  1 0 | 16 * *
.. xx3oo3oo4oo&#x  8  8 | 24  8 0 24 | 32 0 24  0 32 | 16  0 32  0 16 | 1  0 16  0 1 |  * 2 *
.x .x3.o3.o4.o     0 16 |  0  0 8 48 |  0 0  0 24 64 |  0  0  0 32 32 | 0  0  0 16 2 |  * * 1

xx3oo xo3oo3ox&#x   → height = 1/sqrt(2) = 0.707107
(shallower version of: tratet || para-dual tratet)

o.3o. o.3o.3o.    | 12  * |  2  3  3  0  0 | 1  6  3  6  6  3 0  0  0 | 3  6 1  3 12  6  3  3  1 0  0 0 | 3 2  6  3  6  6  2 1 0 0 | 1 3 3 1 2 0
.o3.o .o3.o3.o    |  * 12 |  0  0  3  2  3 | 0  0  0  6  3  6 1  6  3 | 0  0 0  3  6 12  1  3  3 3  6 1 | 0 0  3  6  2  6  6 1 3 2 | 0 1 3 3 2 1
------------------+-------+----------------+--------------------------+---------------------------------+--------------------------+------------
x. .. .. .. ..    |  2  0 | 12  *  *  *  * | 1  3  0  3  0  0 0  0  0 | 3  3 0  3  6  3  0  0  0 0  0 0 | 3 1  6  3  3  3  1 0 0 0 | 1 3 3 1 1 0
.. .. x. .. ..    |  2  0 |  * 18  *  *  * | 0  2  2  0  2  0 0  0  0 | 1  4 1  0  4  0  2  1  0 0  0 0 | 2 2  2  0  4  2  0 1 0 0 | 1 2 1 0 2 0
oo3oo oo3oo3oo&#x |  1  1 |  *  * 36  *  * | 0  0  0  2  2  2 0  0  0 | 0  0 0  1  4  4  1  2  1 0  0 0 | 0 0  2  2  2  4  2 1 0 0 | 0 1 2 1 2 0
.x .. .. .. ..    |  0  2 |  *  *  * 12  * | 0  0  0  3  0  0 1  3  0 | 0  0 0  3  3  6  0  0  0 3  3 0 | 0 0  3  6  1  3  3 0 3 1 | 0 1 3 3 1 1
.. .. .. .. .x    |  0  2 |  *  *  *  * 18 | 0  0  0  0  0  2 0  2  2 | 0  0 0  0  0  4  0  1  2 1  4 1 | 0 0  0  2  0  2  4 1 2 2 | 0 0 1 2 2 1
------------------+-------+----------------+--------------------------+---------------------------------+--------------------------+------------
x.3o. .. .. ..    |  3  0 |  3  0  0  0  0 | 4  *  *  *  *  * *  *  *  3  0 0  3  0  0  0  0  0 0  0 0 | 3 0  6  3  0  0  0 0 0 0 | 1 3 3 1 0 0
x. .. x. .. ..    |  4  0 |  2  2  0  0  0 | * 18  *  *  *  * *  *  * | 1  2 0  0  2  0  0  0  0 0  0 0 | 2 1  2  0  2  1  0 0 0 0 | 1 2 1 0 1 0
.. .. x.3o. ..    |  3  0 |  0  3  0  0  0 | *  * 12  *  *  * *  *  * | 0  2 1  0  0  0  1  0  0 0  0 0 | 1 2  0  0  2  0  0 1 0 0 | 1 1 0 0 2 0
xx .. .. .. ..&#x |  2  2 |  1  0  2  1  0 | *  *  * 36  *  * *  *  * | 0  0 0  1  2  2  0  0  0 0  0 0 | 0 0  2  2  1  2  1 0 0 0 | 0 1 2 1 1 0
.. .. xo .. ..&#x |  2  1 |  0  1  2  0  0 | *  *  *  * 36  * *  *  * | 0  0 0  0  2  0  1  1  0 0  0 0 | 0 0  1  0  2  2  0 1 0 0 | 0 1 1 0 2 0
.. .. .. .. ox&#x |  1  2 |  0  0  2  0  1 | *  *  *  *  * 36 *  *  * | 0  0 0  0  0  2  0  1  1 0  0 0 | 0 0  0  1  0  2  2 1 0 0 | 0 0 1 1 2 0
.x3.o .. .. ..    |  0  3 |  0  0  0  3  0 | *  *  *  *  *  * 4  *  *  0  0 0  3  0  0  0  0  0 3  0 0 | 0 0  3  6  0  0  0 0 3 0 | 0 1 3 3 0 1
.x .. .. .. .x    |  0  4 |  0  0  0  2  2 | *  *  *  *  *  * * 18  * | 0  0 0  0  0  2  0  0  0 1  2 0 | 0 0  0  2  0  1  2 0 2 1 | 0 0 1 2 1 1
.. .. .. .o3.x    |  0  3 |  0  0  0  0  3 | *  *  *  *  *  * *  * 12 | 0  0 0  0  0  0  0  0  1 0  2 1 | 0 0  0  0  0  0  2 1 1 2 | 0 0 0 1 2 1
------------------+-------+----------------+--------------------------+---------------------------------+--------------------------+------------
x.3o. x. .. ..      6  0 |  6  3  0  0  0 | 2  3  0  0  0  0 0  0  0 | 6  * *  *  *  *  *  *  * *  * * | 2 0  2  0  0  0  0 0 0 0 | 1 2 1 0 0 0
x. .. x.3o. ..      6  0 |  3  6  0  0  0 | 0  3  2  0  0  0 0  0  0 | * 12 *  *  *  *  *  *  * *  * * | 1 1  0  0  1  0  0 0 0 0 | 1 1 0 0 1 0
.. .. x.3o.3o.      4  0 |  0  6  0  0  0 | 0  0  4  0  0  0 0  0  0 | *  * 3  *  *  *  *  *  * *  * * | 0 2  0  0  0  0  0 1 0 0 | 1 0 0 0 2 0
xx3oo .. .. ..&#x   3  3 |  3  0  3  3  0 | 1  0  0  3  0  0 1  0  0 | *  * * 12  *  *  *  *  * *  * * | 0 0  2  2  0  0  0 0 0 0 | 0 1 2 1 0 0
xx .. xo .. ..&#x   4  2 |  2  2  4  1  0 | 0  1  0  2  2  0 0  0  0 | *  * *  * 36  *  *  *  * *  * * | 0 0  1  0  1  1  0 0 0 0 | 0 1 1 0 1 0
xx .. .. .. ox&#x   2  4 |  1  0  4  2  2 | 0  0  0  2  0  2 0  1  0 | *  * *  *  * 36  *  *  * *  * * | 0 0  0  1  0  1  1 0 0 0 | 0 0 1 1 1 0
.. .. xo3oo ..&#x   3  1 |  0  3  3  0  0 | 0  0  1  0  3  0 0  0  0 | *  * *  *  *  * 12  *  * *  * * | 0 0  0  0  2  0  0 1 0 0 | 0 1 0 0 2 0
.. .. xo .. ox&#x   2  2 |  0  1  4  0  1 | 0  0  0  0  2  2 0  0  0 | *  * *  *  *  *  * 18  * *  * * | 0 0  0  0  0  2  0 1 0 0 | 0 0 1 0 2 0
.. .. .. oo3ox&#x   1  3 |  0  0  3  0  3 | 0  0  0  0  0  3 0  0  1 | *  * *  *  *  *  *  * 12 *  * * | 0 0  0  0  0  0  2 1 0 0 | 0 0 0 1 2 0
.x3.o .. .. .x      0  6 |  0  0  0  6  3 | 0  0  0  0  0  0 2  3  0 | *  * *  *  *  *  *  *  * 6  * * | 0 0  0  2  0  0  0 0 2 0 | 0 0 1 2 0 1
.x .. .. .o3.x      0  6 |  0  0  0  3  6 | 0  0  0  0  0  0 0  3  2 | *  * *  *  *  *  *  *  * * 12 * | 0 0  0  0  0  0  1 0 1 1 | 0 0 0 1 1 1
.. .. .o3.o3.x      0  4 |  0  0  0  0  6 | 0  0  0  0  0  0 0  0  4 | *  * *  *  *  *  *  *  * *  * 3 | 0 0  0  0  0  0  0 1 0 2 | 0 0 0 0 2 1
------------------+-------+----------------+--------------------------+---------------------------------+--------------------------+------------
x.3o. x.3o. ..      9  0 |  9  9  0  0  0 | 3  9  3  0  0  0 0  0  0 | 3  3 0  0  0  0  0  0  0 0  0 0 | 4 *  *  *  *  *  * * * * | 1 1 0 0 0 0
x. .. x.3o.3o.      8  0 |  4 12  0  0  0 | 0  6  8  0  0  0 0  0  0 | 0  4 2  0  0  0  0  0  0 0  0 0 | * 3  *  *  *  *  * * * * | 1 0 0 0 1 0
xx3oo xo .. ..&#x   6  3 |  6  3  6  3  0 | 2  3  0  6  3  0 1  0  0 | 1  0 0  2  3  0  0  0  0 0  0 0 | * * 12  *  *  *  * * * * | 0 1 1 0 0 0
xx3oo .. .. ox&#x   3  6 |  3  0  6  6  3 | 1  0  0  6  0  3 2  3  0 | 0  0 0  2  0  3  0  0  0 1  0 0 | * *  * 12  *  *  * * * * | 0 0 1 1 0 0
xx .. xo3oo ..&#x   6  2 |  3  6  6  1  0 | 0  3  2  3  6  0 0  0  0 | 0  1 0  0  3  0  2  0  0 0  0 0 | * *  *  * 12  *  * * * * | 0 1 0 0 1 0
xx .. xo .. ox&#x   4  4 |  2  2  8  2  2 | 0  1  0  4  4  4 0  1  0 | 0  0 0  0  2  2  0  2  0 0  0 0 | * *  *  *  * 18  * * * * | 0 0 1 0 1 0
xx .. .. oo3ox&#x   2  6 |  1  0  6  3  6 | 0  0  0  3  0  6 0  3  2 | 0  0 0  0  0  3  0  0  2 0  1 0 | * *  *  *  *  * 12 * * * | 0 0 0 1 1 0
.. .. xo3oo3ox&#x   4  4 |  0  6 12  0  6 | 0  0  4  0 12 12 0  0  4 | 0  0 1  0  0  0  4  6  4 0  0 1 | * *  *  *  *  *  * 3 * * | 0 0 0 0 2 0
.x3.o .. .o3.x      0  9 |  0  0  0  9  9 | 0  0  0  0  0  0 3  9  3 | 0  0 0  0  0  0  0  0  0 3  3 0 | * *  *  *  *  *  * * 4 * | 0 0 0 1 0 1
.x .. .o3.o3.x      0  8 |  0  0  0  4 12 | 0  0  0  0  0  0 0  6  8 | 0  0 0  0  0  0  0  0  0 0  4 2 | * *  *  *  *  *  * * * 3 | 0 0 0 0 1 1
------------------+-------+----------------+--------------------------+---------------------------------+--------------------------+------------
x.3o. x.3o.3o.     12  0 | 12 18  0  0  0 | 4 18 12  0  0  0 0  0  0 | 6 12 3  0  0  0  0  0  0 0  0 0 | 4 3  0  0  0  0  0 0 0 0 | 1 * * * * *
xx3oo xo3oo ..&#x   9  3 |  9  9  9  3  0 | 3  9  3  9  9  0 1  0  0 | 3  3 0  3  9  0  3  0  0 0  0 0 | 1 0  3  0  3  0  0 0 0 0 | * 4 * * * *
xx3oo xo .. ox&#x   6  6 |  6  3 12  6  3 | 2  3  0 12  6  6 2  3  0 | 1  0 0  4  6  6  0  3  0 1  0 0 | 0 0  2  2  0  3  0 0 0 0 | * * 6 * * *
xx3oo .. oo3ox&#x   3  9 |  3  0  9  9  9 | 1  0  0  9  0  9 3  9  3 | 0  0 0  3  0  9  0  0  3 3  3 0 | 0 0  0  3  0  0  3 0 1 0 | * * * 4 * *
xx .. xo3oo3ox&#x   8  8 |  4 12 24  4 12 | 0  6  8 12 24 24 0  6  8 | 0  4 2  0 12 12  8 12  8 0  4 2 | 0 1  0  0  4  6  4 2 0 1 | * * * * 3 *
.x3.o .o3.o3.x      0 12 |  0  0  0 12 18 | 0  0  0  0  0  0 4 18 12 | 0  0 0  0  0  0  0  0  0 6 12 3 | 0 0  0  0  0  0  0 0 4 3 | * * * * * 1

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