x3x        
                   
     x3o        x3o
x3o        x3o     

i.e. a shallow square pyramid with {3} base vertices and a {6} tip

This polyteron also can be obtained as a Stott expansion of squete.

Incidence matrix according to Dynkin symbol

ox ox xo3xx&#x   → height = 1/sqrt(6) = 0.408248
({6} || tisdip)

o. o. o.3o.    | 6  * | 1 1  4 0 0  0 | 1  2  2  4  4 0 0 0 0 | 1 2 2 2 2 4 0 0 0 | 1 1 2 2 0
.o .o .o3.o    | * 12 | 0 0  2 1 1  2 | 0  2  2  1  2 1 2 2 1 | 2 1 2 1 2 1 2 1 1 | 1 2 1 1 1
---------------+------+---------------+-----------------------+-------------------+----------
.. .. x. ..    | 2  0 | 3 *  * * *  * | 1  0  0  4  0 0 0 0 0 | 0 2 0 2 0 4 0 0 0 | 1 0 2 2 0
.. .. .. x.    | 2  0 | * 3  * * *  * | 1  0  0  0  4 0 0 0 0 | 0 0 2 0 2 4 0 0 0 | 0 1 2 2 0
oo oo oo3oo&#x | 1  1 | * * 24 * *  * | 0  1  1  1  1 0 0 0 0 | 1 1 1 1 1 1 0 0 0 | 1 1 1 1 0
.x .. .. ..    | 0  2 | * *  * 6 *  * | 0  2  0  0  0 1 2 0 0 | 2 1 2 0 0 0 2 1 0 | 1 2 1 0 1
.. .x .. ..    | 0  2 | * *  * * 6  * | 0  0  2  0  0 1 0 2 0 | 2 0 0 1 2 0 2 0 1 | 1 2 0 1 1
.. .. .. .x    | 0  2 | * *  * * * 12 | 0  0  0  0  1 0 1 1 1 | 0 0 1 0 1 1 1 1 1 | 0 1 1 1 1
---------------+------+---------------+-----------------------+-------------------+----------
.. .. x.3x.    | 6  0 | 3 3  0 0 0  0 | 1  *  *  *  * * * * * | 0 0 0 0 0 4 0 0 0 | 0 0 2 2 0
ox .. .. ..&#x | 1  2 | 0 0  2 1 0  0 | * 12  *  *  * * * * * | 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0
.. ox .. ..&#x | 1  2 | 0 0  2 0 1  0 | *  * 12  *  * * * * * | 1 0 0 1 1 0 0 0 0 | 1 1 0 1 0
.. .. xo ..&#x | 2  1 | 1 0  2 0 0  0 | *  *  * 12  * * * * * | 0 1 0 1 0 1 0 0 0 | 1 0 1 1 0
.. .. .. xx&#x | 2  2 | 0 1  2 0 0  1 | *  *  *  * 12 * * * * | 0 0 1 0 1 1 0 0 0 | 0 1 1 1 0
.x .x .. ..    | 0  4 | 0 0  0 2 2  0 | *  *  *  *  * 3 * * * | 2 0 0 0 0 0 2 0 0 | 1 2 0 0 1
.x .. .. .x    | 0  4 | 0 0  0 2 0  2 | *  *  *  *  * * 6 * * | 0 0 1 0 0 0 1 1 0 | 0 1 1 0 1
.. .x .. .x    | 0  4 | 0 0  0 0 2  2 | *  *  *  *  * * * 6 * | 0 0 0 0 1 0 1 0 1 | 0 1 0 1 1
.. .. .o3.x    | 0  3 | 0 0  0 0 0  3 | *  *  *  *  * * * * 4 | 0 0 0 0 0 1 0 1 1 | 0 0 1 1 1
---------------+------+---------------+-----------------------+-------------------+----------
ox ox .. ..&#x ♦ 1  4 | 0 0  4 2 2  0 | 0  2  2  0  0 1 0 0 0 | 6 * * * * * * * * | 1 1 0 0 0
ox .. xo ..&#x ♦ 2  2 | 1 0  4 1 0  0 | 0  2  0  2  0 0 0 0 0 | * 6 * * * * * * * | 1 0 1 0 0
ox .. .. xx&#x ♦ 2  4 | 0 1  4 2 0  2 | 0  2  0  0  2 0 1 0 0 | * * 6 * * * * * * | 0 1 1 0 0
.. ox xo ..&#x ♦ 2  2 | 1 0  4 0 1  0 | 0  0  2  2  0 0 0 0 0 | * * * 6 * * * * * | 1 0 0 1 0
.. ox .. xx&#x ♦ 2  4 | 0 1  4 0 2  2 | 0  0  2  0  2 0 0 1 0 | * * * * 6 * * * * | 0 1 0 1 0
.. .. xo3xx&#x ♦ 6  3 | 3 3  6 0 0  3 | 1  0  0  3  3 0 0 0 1 | * * * * * 4 * * * | 0 0 1 1 0
.x .x .. .x    ♦ 0  8 | 0 0  0 4 4  4 | 0  0  0  0  0 2 2 2 0 | * * * * * * 3 * * | 0 1 0 0 1
.x .. .o3.x    ♦ 0  6 | 0 0  0 3 0  6 | 0  0  0  0  0 0 3 0 2 | * * * * * * * 2 * | 0 0 1 0 1
.. .x .o3.x    ♦ 0  6 | 0 0  0 0 3  6 | 0  0  0  0  0 0 0 3 2 | * * * * * * * * 2 | 0 0 0 1 1
---------------+------+---------------+-----------------------+-------------------+----------
ox ox xo ..&#x ♦ 2  4 | 1 0  8 2 2  0 | 0  4  4  4  0 1 0 0 0 | 2 2 0 2 0 0 0 0 0 | 3 * * * *
ox ox .. xx&#x ♦ 2  8 | 0 1  8 4 4  4 | 0  4  4  0  4 2 2 2 0 | 2 0 2 0 2 0 1 0 0 | * 3 * * *
ox .. xo3xx&#x ♦ 6  6 | 3 3 12 3 0  6 | 1  6  0  6  6 0 3 0 2 | 0 3 3 0 0 2 0 1 0 | * * 2 * *
.. ox xo3xx&#x ♦ 6  6 | 3 3 12 0 3  6 | 1  0  6  6  6 0 0 3 2 | 0 0 0 3 3 2 0 0 1 | * * * 2 *
.x .x .o3.x    ♦ 0 12 | 0 0  0 6 6 12 | 0  0  0  0  0 3 6 6 4 | 0 0 0 0 0 0 3 2 2 | * * * * 1

oxx xoo3xxx&#x   → height(1,2) = height(1,3) = sqrt(5/12) = 0.645497
                   height(2,3) = 1
                   height(1,23) = 1/sqrt(6) = 0.408248 ({6} || tisdip)

o.. o..3o..    | 6 * * | 1 1  2  2 0 0 0 0 0 | 1 1 2 2  2 1 2 2 0 0 0 0 0 0 | 1 1 2 1 2 2 1 1 2 0 0 0 0 | 1 1 1 2 1 0
.o. .o.3.o.    | * 6 * | 0 0  2  0 1 2 1 0 0 | 0 2 1 2  2 0 0 0 2 1 1 2 0 0 | 1 2 1 2 1 2 0 0 0 1 2 1 0 | 1 1 2 1 0 1
..o ..o3..o    | * * 6 | 0 0  0  2 0 0 1 1 2 | 0 0 0 0  2 2 1 2 0 0 1 2 2 1 | 0 0 0 2 1 2 1 2 1 0 2 1 1 | 0 1 2 1 1 1
---------------+-------+---------------------+------------------------------+---------------------------+------------
... x.. ...    | 2 0 0 | 3 *  *  * * * * * * | 1 0 2 0  0 0 2 0 0 0 0 0 0 0 | 1 0 2 0 2 0 1 0 2 0 0 0 0 | 1 1 0 2 1 0
... ... x..    | 2 0 0 | * 3  *  * * * * * * | 1 0 0 2  0 0 0 2 0 0 0 0 0 0 | 0 1 2 0 0 2 0 1 2 0 0 0 0 | 1 0 1 2 1 0
oo. oo.3oo.&#x | 1 1 0 | * * 12  * * * * * * | 0 1 1 1  1 0 0 0 0 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 0 0 0 | 1 1 1 1 0 0
o.o o.o3o.o&#x | 1 0 1 | * *  * 12 * * * * * | 0 0 0 0  1 1 1 1 0 0 0 0 0 0 | 0 0 0 1 1 1 1 1 1 0 0 0 0 | 0 1 1 1 1 0
.x. ... ...    | 0 2 0 | * *  *  * 3 * * * * | 0 2 0 0  0 0 0 0 2 0 1 0 0 0 | 1 2 0 2 0 0 0 0 0 1 2 0 0 | 1 1 2 0 0 1
... ... .x.    | 0 2 0 | * *  *  * * 6 * * * | 0 0 0 1  0 0 0 0 1 1 0 1 0 0 | 0 1 1 0 0 1 0 0 0 1 1 1 0 | 1 0 1 1 0 1
.oo .oo3.oo&#x | 0 1 1 | * *  *  * * * 6 * * | 0 0 0 0  2 0 0 0 0 0 1 2 0 0 | 0 0 0 2 1 2 0 0 0 0 2 1 0 | 0 1 2 1 0 1
..x ... ...    | 0 0 2 | * *  *  * * * * 3 * | 0 0 0 0  0 2 0 0 0 0 1 0 2 0 | 0 0 0 2 0 0 1 2 0 0 2 0 1 | 0 1 2 0 1 1
... ... ..x    | 0 0 2 | * *  *  * * * * * 6 | 0 0 0 0  0 0 0 1 0 0 0 1 1 1 | 0 0 0 0 0 1 0 1 1 0 1 1 1 | 0 0 1 1 1 1
---------------+-------+---------------------+------------------------------+---------------------------+------------
... x..3x..    | 6 0 0 | 3 3  0  0 0 0 0 0 0 | 1 * * *  * * * * * * * * * * | 0 0 2 0 0 0 0 0 2 0 0 0 0 | 1 0 0 2 1 0
ox. ... ...&#x | 1 2 0 | 0 0  2  0 1 0 0 0 0 | * 6 * *  * * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
... xo. ...&#x | 2 1 0 | 1 0  2  0 0 0 0 0 0 | * * 6 *  * * * * * * * * * * | 1 0 1 0 1 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0
... ... xx.&#x | 2 2 0 | 0 1  2  0 0 1 0 0 0 | * * * 6  * * * * * * * * * * | 0 1 1 0 0 1 0 0 0 0 0 0 0 | 1 0 1 1 0 0
ooo ooo3ooo&#x | 1 1 1 | 0 0  1  1 0 0 1 0 0 | * * * * 12 * * * * * * * * * | 0 0 0 1 1 1 0 0 0 0 0 0 0 | 0 1 1 1 0 0
o.x ... ...&#x | 1 0 2 | 0 0  0  2 0 0 0 1 0 | * * * *  * 6 * * * * * * * * | 0 0 0 1 0 0 1 1 0 0 0 0 0 | 0 1 1 0 1 0
... x.o ...&#x | 2 0 1 | 1 0  0  2 0 0 0 0 0 | * * * *  * * 6 * * * * * * * | 0 0 0 0 1 0 1 0 1 0 0 0 0 | 0 1 0 1 1 0
... ... x.x&#x | 2 0 2 | 0 1  0  2 0 0 0 0 1 | * * * *  * * * 6 * * * * * * | 0 0 0 0 0 1 0 1 1 0 0 0 0 | 0 0 1 1 1 0
.x. ... .x.    | 0 4 0 | 0 0  0  0 2 2 0 0 0 | * * * *  * * * * 3 * * * * * | 0 1 0 0 0 0 0 0 0 1 1 0 0 | 1 0 1 0 0 1
... .o.3.x.    | 0 3 0 | 0 0  0  0 0 3 0 0 0 | * * * *  * * * * * 2 * * * * | 0 0 1 0 0 0 0 0 0 1 0 1 0 | 1 0 0 1 0 1
.xx ... ...&#x | 0 2 2 | 0 0  0  0 1 0 2 1 0 | * * * *  * * * * * * 3 * * * | 0 0 0 2 0 0 0 0 0 0 2 0 0 | 0 1 2 0 0 1
... ... .xx&#x | 0 2 2 | 0 0  0  0 0 1 2 0 1 | * * * *  * * * * * * * 6 * * | 0 0 0 0 0 1 0 0 0 0 1 1 0 | 0 0 1 1 0 1
..x ... ..x    | 0 0 4 | 0 0  0  0 0 0 0 2 2 | * * * *  * * * * * * * * 3 * | 0 0 0 0 0 0 0 1 0 0 1 0 1 | 0 0 1 0 1 1
... ..o3..x    | 0 0 3 | 0 0  0  0 0 0 0 0 3 | * * * *  * * * * * * * * * 2 | 0 0 0 0 0 0 0 0 1 0 0 1 1 | 0 0 0 1 1 1
---------------+-------+---------------------+------------------------------+---------------------------+------------
ox. xo. ...&#x ♦ 2 2 0 | 1 0  4  0 1 0 0 0 0 | 0 2 2 0  0 0 0 0 0 0 0 0 0 0 | 3 * * * * * * * * * * * * | 1 1 0 0 0 0
ox. ... xx.&#x ♦ 2 4 0 | 0 1  4  0 2 2 0 0 0 | 0 2 0 2  0 0 0 0 1 0 0 0 0 0 | * 3 * * * * * * * * * * * | 1 0 1 0 0 0
... xo.3xx.&#x ♦ 6 3 0 | 3 3  6  0 0 3 0 0 0 | 1 0 3 3  0 0 0 0 0 1 0 0 0 0 | * * 2 * * * * * * * * * * | 1 0 0 1 0 0
oxx ... ...&#x ♦ 1 2 2 | 0 0  2  2 1 0 2 1 0 | 0 1 0 0  2 1 0 0 0 0 1 0 0 0 | * * * 6 * * * * * * * * * | 0 1 1 0 0 0
... xoo ...&#x ♦ 2 1 1 | 1 0  2  2 0 0 1 0 0 | 0 0 1 0  2 0 1 0 0 0 0 0 0 0 | * * * * 6 * * * * * * * * | 0 1 0 1 0 0
... ... xxx&#x ♦ 2 2 2 | 0 1  2  2 0 1 2 0 1 | 0 0 0 1  2 0 0 1 0 0 0 1 0 0 | * * * * * 6 * * * * * * * | 0 0 1 1 0 0
o.x x.o ...&#x ♦ 2 0 2 | 1 0  0  4 0 0 0 1 0 | 0 0 0 0  0 2 2 0 0 0 0 0 0 0 | * * * * * * 3 * * * * * * | 0 1 0 0 1 0
o.x ... x.x&#x ♦ 2 0 4 | 0 1  0  4 0 0 0 2 2 | 0 0 0 0  0 2 0 2 0 0 0 0 1 0 | * * * * * * * 3 * * * * * | 0 0 1 0 1 0
... x.o3x.x&#x ♦ 6 0 3 | 3 3  0  6 0 0 0 0 3 | 1 0 0 0  0 0 3 3 0 0 0 0 0 1 | * * * * * * * * 2 * * * * | 0 0 0 1 1 0
.x. .o.3.x.    ♦ 0 6 0 | 0 0  0  0 3 6 0 0 0 | 0 0 0 0  0 0 0 0 3 2 0 0 0 0 | * * * * * * * * * 1 * * * | 1 0 0 0 0 1
.xx ... .xx&#x ♦ 0 4 4 | 0 0  0  0 2 2 4 2 2 | 0 0 0 0  0 0 0 0 1 0 2 2 1 0 | * * * * * * * * * * 3 * * | 0 0 1 0 0 1
... .oo3.xx&#x ♦ 0 3 3 | 0 0  0  0 0 3 3 0 3 | 0 0 0 0  0 0 0 0 0 1 0 3 0 1 | * * * * * * * * * * * 2 * | 0 0 0 1 0 1
..x ..o3..x    ♦ 0 0 6 | 0 0  0  0 0 0 0 3 6 | 0 0 0 0  0 0 0 0 0 0 0 0 3 2 | * * * * * * * * * * * * 1 | 0 0 0 0 1 1
---------------+-------+---------------------+------------------------------+---------------------------+------------
ox. xo.3xx.&#x ♦ 6 6 0 | 3 3 12  0 3 6 0 0 0 | 1 6 6 6  0 0 0 0 3 2 0 0 0 0 | 3 3 2 0 0 0 0 0 0 1 0 0 0 | 1 * * * * *
oxx xoo ...&#x ♦ 2 2 2 | 1 0  4  4 1 0 2 1 0 | 0 2 2 0  4 2 2 0 0 0 1 0 0 0 | 1 0 0 2 2 0 1 0 0 0 0 0 0 | * 3 * * * *
oxx ... xxx&#x ♦ 2 4 4 | 0 1  4  4 2 2 4 2 2 | 0 2 0 2  4 2 0 2 1 0 2 2 1 0 | 0 1 0 2 0 2 0 1 0 0 1 0 0 | * * 3 * * *
... xoo3xxx&#x ♦ 6 3 3 | 3 3  6  6 0 3 3 0 3 | 1 0 3 3  6 0 3 3 0 1 0 3 0 1 | 0 0 1 0 3 3 0 0 1 0 0 1 0 | * * * 2 * *
o.x x.o3x.x&#x ♦ 6 0 6 | 3 3  0 12 0 0 0 3 6 | 1 0 0 0  0 6 6 6 0 0 0 0 3 2 | 0 0 0 0 0 0 3 3 2 0 0 0 1 | * * * * 1 *
.xx .oo3.xx&#x ♦ 0 6 6 | 0 0  0  0 3 6 6 3 6 | 0 0 0 0  0 0 0 0 3 2 3 6 3 2 | 0 0 0 0 0 0 0 0 0 1 3 2 1 | * * * * * 1