Acronym squatut
Name square - truncated-tetrahedron duoprism
Circumradius sqrt(15/8) = 1.369306
Confer
more general:
n,tut-dip  
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

x4o x3x3o

. . . . . | 48 |  2  1  2 |  1  2  4  2  1 | 1  2  4  2 1 | 2 1 2
----------+----+----------+----------------+--------------+------
x . . . . |  2 | 48  *  * |  1  1  2  0  0 | 1  2  2  1 0 | 2 1 1
. . x . . |  2 |  * 24  * |  0  2  0  2  0 | 1  0  4  0 1 | 2 0 2
. . . x . |  2 |  *  * 48 |  0  0  2  1  1 | 0  1  2  2 1 | 1 1 2
----------+----+----------+----------------+--------------+------
x4o . . . |  4 |  4  0  0 | 12  *  *  *  * | 1  2  0  0 0 | 2 1 0
x . x . . |  4 |  2  2  0 |  * 24  *  *  * | 1  0  2  0 0 | 2 0 1
x . . x . |  4 |  2  0  2 |  *  * 48  *  * | 0  1  1  1 0 | 1 1 1
. . x3x . |  6 |  0  3  3 |  *  *  * 16  * | 0  0  2  0 1 | 1 0 2
. . . x3o |  3 |  0  0  3 |  *  *  *  * 16 | 0  0  0  2 1 | 0 1 2
----------+----+----------+----------------+--------------+------
x4o x . .   8 |  8  4  0 |  2  4  0  0  0 | 6  *  *  * * | 2 0 0
x4o . x .   8 |  8  0  4 |  2  0  4  0  0 | * 12  *  * * | 1 1 0
x . x3x .  12 |  6  6  6 |  0  3  3  2  0 | *  * 16  * * | 1 0 1
x . . x3o   6 |  3  0  6 |  0  0  3  0  2 | *  *  * 16 * | 0 1 1
. . x3x3o  12 |  0  6 12 |  0  0  0  4  4 | *  *  *  * 4 | 0 0 2
----------+----+----------+----------------+--------------+------
x4o x3x .  24 | 24 12 12 |  6 12 12  4  0 | 3  3  4  0 0 | 4 * *
x4o . x3o  12 | 12  0 12 |  3  0 12  0  4 | 0  3  0  4 0 | * 4 *
x . x3x3o  24 | 12 12 24 |  0  6 12  8  8 | 0  0  4  4 2 | * * 4

x x x3x3o

. . . . . | 48 |  1  1  1  2 |  1  1  2  1  2  2  1 | 1  2 2 1 2 1 1 | 2 1 1 1
----------+----+-------------+----------------------+----------------+--------
x . . . . |  2 | 24  *  *  * |  1  1  2  0  0  0  0 | 1  2 2 1 0 0 0 | 2 1 1 0
. x . . . |  2 |  * 24  *  * |  1  0  0  1  2  0  0 | 1  2 0 0 2 1 0 | 2 1 0 1
. . x . . |  2 |  *  * 24  * |  0  1  0  1  0  2  0 | 1  0 2 0 2 0 1 | 2 0 1 1
. . . x . |  2 |  *  *  * 48 |  0  0  1  0  1  1  1 | 0  1 1 1 1 1 1 | 1 1 1 1
----------+----+-------------+----------------------+----------------+--------
x x . . . |  4 |  2  2  0  0 | 12  *  *  *  *  *  * | 1  2 0 0 0 0 0 | 2 1 0 0
x . x . . |  4 |  2  0  2  0 |  * 12  *  *  *  *  * | 1  0 2 0 0 0 0 | 2 0 1 0
x . . x . |  4 |  2  0  0  2 |  *  * 24  *  *  *  * | 0  1 1 1 0 0 0 | 1 1 1 0
. x x . . |  4 |  0  2  2  0 |  *  *  * 12  *  *  * | 1  0 0 0 2 0 0 | 2 0 0 1
. x . x . |  4 |  0  2  0  2 |  *  *  *  * 24  *  * | 0  1 0 0 1 1 0 | 1 1 0 1
. . x3x . |  6 |  0  0  3  3 |  *  *  *  *  * 16  * | 0  0 1 0 1 0 1 | 1 0 1 1
. . . x3o |  3 |  0  0  0  3 |  *  *  *  *  *  * 16 | 0  0 0 1 0 1 1 | 0 1 1 1
----------+----+-------------+----------------------+----------------+--------
x x x . .   8 |  4  4  4  0 |  2  2  0  2  0  0  0 | 6  * * * * * * | 2 0 0 0
x x . x .   8 |  4  4  0  4 |  2  0  2  0  2  0  0 | * 12 * * * * * | 1 1 0 0
x . x3x .  12 |  6  0  6  6 |  0  3  3  0  0  2  0 | *  * 8 * * * * | 1 0 1 0
x . . x3o   6 |  3  0  0  6 |  0  0  3  0  0  0  2 | *  * * 8 * * * | 0 1 1 0
. x x3x .  12 |  0  6  6  6 |  0  0  0  3  3  2  0 | *  * * * 8 * * | 1 0 0 1
. x . x3o   6 |  0  3  0  6 |  0  0  0  0  3  0  2 | *  * * * * 8 * | 0 1 0 1
. . x3x3o  12 |  0  0  6 12 |  0  0  0  0  0  4  4 | *  * * * * * 4 | 0 0 1 1
----------+----+-------------+----------------------+----------------+--------
x x x3x .  24 | 12 12 12 12 |  6  6  6  6  6  4  0 | 3  3 2 0 2 0 0 | 4 * * *
x x . x3o  12 |  6  6  0 12 |  3  0  6  0  6  0  4 | 0  3 0 2 0 2 0 | * 4 * *
x . x3x3o  24 | 12  0 12 24 |  0  6 12  0  0  8  8 | 0  0 4 4 0 0 2 | * * 2 *
. x x3x3o  24 |  0 12 12 24 |  0  0  0  6 12  8  8 | 0  0 0 0 4 4 2 | * * * 2

xx oo3xx3xx&#x   → height = 1
(tuttip || tuttip)

o. o.3o.3o.    | 24  * |  1  2  1  1  0  0  0 |  2 1 1 2  1  2  1  0 0 0 0 | 1 2 1  2 1 1 2 0 0 0 | 1 1 2 1 0
.o .o3.o3.o    |  * 24 |  0  0  0  1  1  2  1 |  0 0 0 0  1  2  1  2 1 1 2 | 0 0 0  2 1 1 2 1 2 1 | 0 1 2 1 1
---------------+-------+----------------------+----------------------------+----------------------+----------
x. .. .. ..    |  2  0 | 12  *  *  *  *  *  * |  2 1 0 0  1  0  0  0 0 0 0 | 1 2 0  2 1 0 0 0 0 0 | 1 1 2 0 0
.. .. x. ..    |  2  0 |  * 24  *  *  *  *  * |  1 0 1 1  0  1  0  0 0 0 0 | 1 1 1  1 0 1 1 0 0 0 | 1 1 1 1 0
.. .. .. x.    |  2  0 |  *  * 12  *  *  *  * |  0 1 0 2  0  0  1  0 0 0 0 | 0 2 1  0 1 0 2 0 0 0 | 1 0 2 1 0
oo oo3oo3oo&#x |  1  1 |  *  *  * 24  *  *  * |  0 0 0 0  1  2  1  0 0 0 0 | 0 0 0  2 1 1 2 0 0 0 | 0 1 2 1 0
.x .. .. ..    |  0  2 |  *  *  *  * 12  *  * |  0 0 0 0  1  0  0  2 1 0 0 | 0 0 0  2 1 0 0 1 2 0 | 0 1 2 0 1
.. .. .x ..    |  0  2 |  *  *  *  *  * 24  * |  0 0 0 0  0  1  0  1 0 1 1 | 0 0 0  1 0 1 1 1 1 1 | 0 1 1 1 1
.. .. .. .x    |  0  2 |  *  *  *  *  *  * 12 |  0 0 0 0  0  0  1  0 1 0 2 | 0 0 0  0 1 0 2 0 2 1 | 0 0 2 1 1
---------------+-------+----------------------+----------------------------+----------------------+----------
x. .. x. ..    |  4  0 |  2  2  0  0  0  0  0 | 12 * * *  *  *  *  * * * * | 1 1 0  1 0 0 0 0 0 0 | 1 1 1 0 0
x. .. .. x.    |  4  0 |  2  0  2  0  0  0  0 |  * 6 * *  *  *  *  * * * * | 0 2 0  0 1 0 0 0 0 0 | 1 0 2 0 0
.. o.3x. ..    |  3  0 |  0  3  0  0  0  0  0 |  * * 8 *  *  *  *  * * * * | 1 0 1  0 0 1 0 0 0 0 | 1 1 0 1 0
.. .. x.3x.    |  6  0 |  0  3  3  0  0  0  0 |  * * * 8  *  *  *  * * * * | 0 1 1  0 0 0 1 0 0 0 | 1 0 1 1 0
xx .. .. ..&#x |  2  2 |  1  0  0  2  1  0  0 |  * * * * 12  *  *  * * * * | 0 0 0  2 1 0 0 0 0 0 | 0 1 2 0 0
.. .. xx ..&#x |  2  2 |  0  1  0  2  0  1  0 |  * * * *  * 24  *  * * * * | 0 0 0  1 0 1 1 0 0 0 | 0 1 1 1 0
.. .. .. xx&#x |  2  2 |  0  0  1  2  0  0  1 |  * * * *  *  * 12  * * * * | 0 0 0  0 1 0 2 0 0 0 | 0 0 2 1 0
.x .. .x ..    |  0  4 |  0  0  0  0  2  2  0 |  * * * *  *  *  * 12 * * * | 0 0 0  1 0 0 0 1 1 0 | 0 1 1 0 1
.x .. .. .x    |  0  4 |  0  0  0  0  2  0  2 |  * * * *  *  *  *  * 6 * * | 0 0 0  0 1 0 0 0 2 0 | 0 0 2 0 1
.. .o3.x ..    |  0  3 |  0  0  0  0  0  3  0 |  * * * *  *  *  *  * * 8 * | 0 0 0  0 0 1 0 1 0 1 | 0 1 0 1 1
.. .. .x3.x    |  0  6 |  0  0  0  0  0  3  3 |  * * * *  *  *  *  * * * 8 | 0 0 0  0 0 0 1 0 1 1 | 0 0 1 1 1
---------------+-------+----------------------+----------------------------+----------------------+----------
x. o.3x. ..      6  0 |  3  6  0  0  0  0  0 |  3 0 2 0  0  0  0  0 0 0 0 | 4 * *  * * * * * * * | 1 1 0 0 0
x. .. x.3x.     12  0 |  6  6  6  0  0  0  0 |  3 3 0 2  0  0  0  0 0 0 0 | * 4 *  * * * * * * * | 1 0 1 0 0
.. o.3x.3x.     12  0 |  0 12  6  0  0  0  0 |  0 0 4 4  0  0  0  0 0 0 0 | * * 2  * * * * * * * | 1 0 0 1 0
xx .. xx ..&#x   4  4 |  2  2  0  4  2  2  0 |  1 0 0 0  2  2  0  1 0 0 0 | * * * 12 * * * * * * | 0 1 1 0 0
xx .. .. xx&#x   4  4 |  2  0  2  4  2  0  2 |  0 1 0 0  2  0  2  0 1 0 0 | * * *  * 6 * * * * * | 0 0 2 0 0
.. oo3xx ..&#x   3  3 |  0  3  0  3  0  3  0 |  0 0 1 0  0  3  0  0 0 1 0 | * * *  * * 8 * * * * | 0 1 0 1 0
.. .. xx3xx&#x   6  6 |  0  3  3  6  0  3  3 |  0 0 0 1  0  3  3  0 0 0 1 | * * *  * * * 8 * * * | 0 0 1 1 0
.x .o3.x ..      0  6 |  0  0  0  0  3  6  0 |  0 0 0 0  0  0  0  3 0 2 0 | * * *  * * * * 4 * * | 0 1 0 0 1
.x .. .x3.x      0 12 |  0  0  0  0  6  6  6 |  0 0 0 0  0  0  0  3 3 0 2 | * * *  * * * * * 4 * | 0 0 1 0 1
.. .o3.x3.x      0 12 |  0  0  0  0  0 12  6 |  0 0 0 0  0  0  0  0 0 4 4 | * * *  * * * * * * 2 | 0 0 0 1 1
---------------+-------+----------------------+----------------------------+----------------------+----------
x. o.3x.3x.     24  0 | 12 24 12  0  0  0  0 | 12 6 8 8  0  0  0  0 0 0 0 | 4 4 2  0 0 0 0 0 0 0 | 1 * * * *
xx oo3xx ..&#x   6  6 |  3  6  0  6  3  6  0 |  3 0 2 0  3  6  0  3 0 2 0 | 1 0 0  3 0 2 0 1 0 0 | * 4 * * *
xx .. xx3xx&#x  12 12 |  6  6  6 12  6  6  6 |  3 3 0 2  6  6  6  3 3 0 2 | 0 1 0  3 3 0 2 0 1 0 | * * 4 * *
.. oo3xx3xx&#x  12 12 |  0 12  6 12  0 12  6 |  0 0 4 4  0 12  6  0 0 4 4 | 0 0 1  0 0 4 4 0 0 1 | * * * 2 *
.x .o3.x3.x      0 24 |  0  0  0  0 12 24 12 |  0 0 0 0  0  0  0 12 6 8 8 | 0 0 0  0 0 0 0 4 4 2 | * * * * 1

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