This polypeton is topologically its own dual.

Considering one of the vertices of tet as a tip atop the square instead, one recognizes this figure to be likewise the pyramid product of {3} with squippy. Then it could be seen too as a diminishing of octete.

Incidence matrix according to Dynkin symbol

xo4oo ox3oo3oo&#x   → height = 1/sqrt(8) = 0.353553
({4} || perp tet)

o.4o. o.3o.3o.    | 4 * | 2  4 0 | 1  8  6 0 | 4 12  4 0 | 6  8 1 | 4 2
.o4.o .o3.o3.o    | * 4 ♦ 0  4 3 | 0  4 12 3 | 1 12 12 1 | 3 12 4 | 3 4
------------------+-----+--------+-----------+-----------+--------+----
x. .. .. .. ..    | 2 0 | 4  * * | 1  4  0 0 | 4  6  0 0 | 6  4 0 | 4 1
oo4oo oo3oo3oo&#x | 1 1 | * 16 * | 0  2  3 0 | 1  6  3 0 | 3  6 1 | 3 2
.. .. .x .. ..    | 0 2 | *  * 6 ♦ 0  0  4 2 | 0  4  8 1 | 1  8 4 | 2 4
------------------+-----+--------+-----------+-----------+--------+----
x.4o. .. .. ..    | 4 0 | 4  0 0 | 1  *  * * ♦ 4  0  0 0 | 6  0 0 | 4 0
xo .. .. .. ..&#x | 2 1 | 1  2 0 | * 16  * * | 1  3  0 0 | 3  3 0 | 3 1
.. .. ox .. ..&#x | 1 2 | 0  2 1 | *  * 24 * | 0  2  2 0 | 1  4 1 | 2 2
.. .. .x3.o ..    | 0 3 | 0  0 3 | *  *  * 4 ♦ 0  0  4 1 | 0  4 4 | 1 4
------------------+-----+--------+-----------+-----------+--------+----
xo4oo .. .. ..&#x ♦ 4 1 | 4  4 0 | 1  4  0 0 | 4  *  * * | 3  0 0 | 3 0
xo .. ox .. ..&#x ♦ 2 2 | 1  4 1 | 0  2  2 0 | * 24  * * | 1  2 0 | 2 1
.. .. ox3oo ..&#x ♦ 1 3 | 0  3 3 | 0  0  3 1 | *  * 16 * | 0  2 1 | 1 2
.. .. .x3.o3.o    ♦ 0 4 | 0  0 6 | 0  0  0 4 | *  *  * 1 | 0  0 4 | 0 4
------------------+-----+--------+-----------+-----------+--------+----
xo4oo ox .. ..&#x ♦ 4 2 | 4  8 1 | 1  8  4 0 | 2  4  0 0 | 6  * * | 2 0
xo .. ox3oo ..&#x ♦ 2 3 | 1  6 3 | 0  3  6 1 | 0  3  2 0 | * 16 * | 1 1
.. .. ox3oo3oo&#x ♦ 1 4 | 0  4 6 | 0  0  6 4 | 0  0  4 1 | *  * 4 | 0 2
------------------+-----+--------+-----------+-----------+--------+----
xo4oo ox3oo ..&#x ♦ 4 3 | 4 12 3 | 1 12 12 1 | 3 12  4 0 | 3  4 0 | 4 *
xo .. ox3oo3oo&#x ♦ 2 4 | 1  8 6 | 0  4 12 4 | 0  6  8 1 | 0  4 2 | * 4

xo xo ox3oo3ooamp;#x   → height = 1/sqrt(8) = 0.353553
({4} || perp tet)

o. o. o.3o.3o.    | 4 * | 1 1  4 0 | 1 4 4  6 0 | 4  6  6  4 0 | 6 4 4 1 | 4 1 1
.o .o .o3.o3.o    | * 4 ♦ 0 0  4 3 | 0 2 2 12 3 | 1  6  6 12 1 | 3 6 6 4 | 3 2 2
------------------+-----+----------+------------+--------------+---------+------
x. .. .. .. ..    | 2 0 | 2 *  * * | 1 4 0  0 0 | 4  6  0  0 0 | 6 4 0 0 | 4 1 0
.. x. .. .. ..    | 2 0 | * 2  * * | 1 0 4  0 0 | 4  0  6  0 0 | 6 0 4 0 | 4 0 1
oo4oo oo3oo3oo&#x | 1 1 | * * 16 * | 0 1 1  3 0 | 1  3  3  3 0 | 3 3 3 1 | 3 1 1
.. .. .x .. ..    | 0 2 | * *  * 6 ♦ 0 0 0  4 2 | 0  2  2  8 1 | 1 4 4 4 | 2 2 2
------------------+-----+----------+------------+--------------+---------+------
x. x. .. .. ..    | 4 0 | 2 2  0 0 | 1 * *  * * ♦ 4  0  0  0 0 | 6 0 0 0 | 4 0 0
xo .. .. .. ..&#x | 2 1 | 1 0  2 0 | * 8 *  * * | 1  3  0  0 0 | 3 3 0 0 | 3 1 0
.. xo .. .. ..&#x | 2 1 | 0 1  2 0 | * * 8  * * | 1  0  3  0 0 | 3 0 3 0 | 3 0 1
.. .. ox .. ..&#x | 1 2 | 0 0  2 1 | * * * 24 * | 0  1  1  2 0 | 1 2 2 1 | 2 1 1
.. .. .x3.o ..    | 0 3 | 0 0  0 3 | * * *  * 4 ♦ 0  0  0  4 1 | 0 2 2 4 | 1 2 2
------------------+-----+----------+------------+--------------+---------+------
xo xo .. .. ..&#x ♦ 4 1 | 2 2  4 0 | 1 2 2  0 0 | 4  *  *  * * | 3 0 0 0 | 3 0 0
xo .. ox .. ..&#x ♦ 2 2 | 1 0  4 1 | 0 2 0  2 0 | * 12  *  * * | 1 2 0 0 | 2 1 0
.. xo ox .. ..&#x ♦ 2 2 | 0 1  4 1 | 0 0 2  2 0 | *  * 12  * * | 1 0 2 0 | 2 0 1
.. .. ox3oo ..&#x ♦ 1 3 | 0 0  3 3 | 0 0 0  3 1 | *  *  * 16 * | 0 1 1 1 | 1 1 1
.. .. .x3.o3.o    ♦ 0 4 | 0 0  0 6 | 0 0 0  0 4 | *  *  *  * 1 | 0 0 0 4 | 0 2 2
------------------+-----+----------+------------+--------------+---------+------
xo xo ox .. ..&#x ♦ 4 2 | 2 2  8 1 | 1 4 4  4 0 | 2  2  2  0 0 | 6 * * * | 2 0 0
xo .. ox3oo ..&#x ♦ 2 3 | 1 0  6 3 | 0 3 0  6 1 | 0  3  0  2 0 | * 8 * * | 1 1 0
.. xo ox3oo ..&#x ♦ 2 3 | 0 1  6 3 | 0 0 3  6 1 | 0  0  3  2 0 | * * 8 * | 1 0 1
.. .. ox3oo3oo&#x ♦ 1 4 | 0 0  4 6 | 0 0 0  6 4 | 0  0  0  4 1 | * * * 4 | 0 1 1
------------------+-----+----------+------------+--------------+---------+------
xo xo ox3oo ..&#x ♦ 4 3 | 2 2 12 3 | 1 6 6 12 1 | 3  6  6  4 0 | 3 2 2 0 | 4 * *
xo .. ox3oo3oo&#x ♦ 2 4 | 1 0  8 6 | 0 4 0 12 4 | 0  6  0  8 1 | 0 4 0 2 | * 2 *
.. xo ox3oo3oo&#x ♦ 2 4 | 0 1  8 6 | 0 0 4 12 4 | 0  0  6  8 1 | 0 0 4 2 | * * 2

oxx xoo3ooo3ooo&#x   → height(1,2) = height(1,3) = sqrt(3/8) = 0.612372
                       height(2,3) = 1

o.. o..3o..3o..    | 4 * * ♦ 3 2 2 0 0 0 | 3 1  6 2 1  6 0 | 1 3 6 1  6 3 6 | 3 2 3 6 3 2 | 1 3 2 1
.o. .o.3.o.3.o.    | * 2 * | 0 4 0 1 1 0 | 0 4  6 4 0  0 1 | 0 6 4 4  6 0 0 | 4 1 6 4 0 0 | 1 4 1 0
..o ..o3..o3..o    | * * 2 | 0 0 4 0 1 1 | 0 0  0 4 4  6 1 | 0 0 0 4  6 6 4 | 0 0 6 4 4 1 | 0 4 1 1
-------------------+-------+-------------+-----------------+----------------+-------------+--------
... x.. ... ...    | 2 0 0 | 6 * * * * * ♦ 2 0  2 0 0  2 0 | 1 1 4 0  2 1 4 | 2 2 1 4 2 2 | 1 2 2 1
oo. oo.3oo.3oo.&#x | 1 1 0 | * 8 * * * * | 0 1  3 1 0  0 0 | 0 3 3 1  3 0 0 | 3 1 3 3 0 0 | 1 3 1 0
o.o o.o3o.o3o.o&#x | 1 0 1 | * * 8 * * * | 0 0  0 1 1  3 0 | 0 0 0 1  3 3 3 | 0 0 3 3 3 1 | 0 3 1 1
.x. ... ... ...    | 0 2 0 | * * * 1 * * | 0 4  0 0 0  0 1 | 0 6 0 4  0 0 0 | 4 0 6 0 0 0 | 1 4 0 0
.oo .oo3.oo3.oo&#x | 0 1 1 | * * * * 2 * | 0 0  0 4 0  0 1 | 0 0 0 4  6 0 0 | 0 0 6 4 0 0 | 0 4 1 0
..x ... ... ...    | 0 0 2 | * * * * * 1 | 0 0  0 0 4  0 1 | 0 0 0 4  0 6 0 | 0 0 6 0 4 0 | 0 4 0 1
-------------------+-------+-------------+-----------------+----------------+-------------+--------
... x..3o.. ...    | 3 0 0 | 3 0 0 0 0 0 | 4 *  * * *  * * ♦ 1 0 2 0  0 0 2 | 1 2 0 2 1 2 | 1 1 2 1
ox. ... ... ...&#x | 1 2 0 | 0 2 0 1 0 0 | * 4  * * *  * * | 0 3 0 1  0 0 0 | 3 0 3 0 0 0 | 1 3 0 0
... xo. ... ...&#x | 2 1 0 | 1 2 0 0 0 0 | * * 12 * *  * * | 0 1 2 0  1 0 0 | 2 1 1 2 0 0 | 1 2 1 0
ooo ooo3ooo3ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * *  * 8 *  * * | 0 0 0 1  3 0 0 | 0 0 3 3 0 0 | 0 3 1 0
o.x ... ... ...&#x | 1 0 2 | 0 0 2 0 0 1 | * *  * * 4  * * | 0 0 0 1  0 3 0 | 0 0 3 0 3 0 | 0 3 0 1
... x.o ... ...&#x | 2 0 1 | 1 0 2 0 0 0 | * *  * * * 12 * | 0 0 0 0  1 1 2 | 0 0 1 2 2 1 | 0 2 1 1
.xx ... ... ...&#x | 0 2 2 | 0 0 0 1 2 1 | * *  * * *  * 1 ♦ 0 0 0 4  0 0 0 | 0 0 6 0 0 0 | 0 4 0 0
-------------------+-------+-------------+-----------------+----------------+-------------+--------
... x..3o..3o..    ♦ 4 0 0 | 6 0 0 0 0 0 | 4 0  0 0 0  0 0 | 1 * * *  * * * | 0 2 0 0 0 2 | 1 0 2 1
ox. xo. ... ...&#x ♦ 2 2 0 | 1 4 0 1 0 0 | 0 2  2 0 0  0 0 | * 6 * *  * * * | 2 0 1 0 0 0 | 1 2 0 0
... xo.3oo. ...&#x ♦ 3 1 0 | 3 3 0 0 0 0 | 1 0  3 0 0  0 0 | * * 8 *  * * * | 1 1 0 1 0 0 | 1 1 1 0
oxx ... ... ...&#x ♦ 1 2 2 | 0 2 2 1 2 1 | 0 1  0 2 1  0 1 | * * * 4  * * * | 0 0 3 0 0 0 | 0 3 0 0
... xoo ... ...&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 0 0  1 2 0  1 0 | * * * * 12 * * | 0 0 1 2 0 0 | 0 2 1 0
o.x x.o ... ...&#x ♦ 2 0 2 | 1 0 4 0 0 1 | 0 0  0 0 2  2 0 | * * * *  * 6 * | 0 0 1 0 2 0 | 0 2 0 1
... x.o3o.o ...&#x ♦ 3 0 1 | 3 0 3 0 0 0 | 1 0  0 0 0  3 0 | * * * *  * * 8 | 0 0 0 1 1 1 | 0 1 1 1
-------------------+-------+-------------+-----------------+----------------+-------------+--------
ox. xo.3oo. ...&#x ♦ 3 2 0 | 3 6 0 1 0 0 | 1 3  6 0 0  0 0 | 0 3 2 0  0 0 0 | 4 * * * * * | 1 1 0 0
... xo.3oo.3oo.&#x ♦ 4 1 0 | 6 4 0 0 0 0 | 4 0  6 0 0  0 0 | 1 0 4 0  0 0 0 | * 2 * * * * | 1 0 1 0
oxx xoo ... ...&#x ♦ 2 2 2 | 1 4 4 1 2 1 | 0 2  2 4 2  2 1 | 0 1 0 2  2 1 0 | * * 6 * * * | 0 2 0 0
... xoo3ooo ...&#x ♦ 3 1 1 | 3 3 3 0 1 0 | 1 0  3 3 0  3 0 | 0 0 1 0  3 0 1 | * * * 8 * * | 0 1 1 0
o.x x.o3o.o ...&#x ♦ 3 0 2 | 3 0 6 0 0 1 | 1 0  0 0 3  6 0 | 0 0 0 0  0 3 2 | * * * * 4 * | 0 1 0 1
... x.o3o.o3o.o&#x ♦ 4 0 1 | 6 0 4 0 0 0 | 4 0  0 0 0  6 0 | 1 0 0 0  0 0 4 | * * * * * 2 | 0 0 1 1
-------------------+-------+-------------+-----------------+----------------+-------------+--------
ox. xo.3oo.3oo.&#x ♦ 4 2 0 | 6 8 0 1 0 0 | 4 4 12 0 0  0 0 | 1 6 8 0  0 0 0 | 4 2 0 0 0 0 | 1 * * *
oxx xoo3ooo ...&#x ♦ 3 2 2 | 3 6 6 1 2 1 | 1 3  6 6 3  6 1 | 0 3 2 3  6 3 2 | 1 0 3 2 1 0 | * 4 * *
... xoo3ooo3ooo&#x ♦ 4 1 1 | 6 4 4 0 1 0 | 4 0  6 4 0  6 0 | 1 0 4 0  6 0 4 | 0 1 0 4 0 1 | * * 2 *
o.x x.o3o.o3o.o&#x ♦ 4 0 2 | 6 0 8 0 0 1 | 4 0  0 0 4 12 0 | 1 0 0 0  0 6 8 | 0 0 0 0 4 2 | * * * 1