x3o       
                 
    x3x       x3x
x3x       x3x    

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

Incidence matrix according to Dynkin symbol

ox ox ox3xx&#x   → height = 1/sqrt(6) = 0.408248
({3} || shiddip)

o. o. o.3o.    | 3  * | 2  8  0  0  0  0 | 1  4  4  4  8 0 0 0 0 0 0 | 2 2 4 2 4 4 0 0 0 0 | 1 2 2 2 0
.o .o .o3.o    | * 24 | 0  1  1  1  1  1 | 0  1  1  1  1 1 1 1 1 1 1 | 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1
---------------+------+------------------+---------------------------+---------------------+----------
.. .. .. x.    | 2  0 | 3  *  *  *  *  * | 1  0  0  0  4 0 0 0 0 0 0 | 0 0 2 0 2 4 0 0 0 0 | 0 1 2 2 0
oo oo oo3oo&#x | 1  1 | * 24  *  *  *  * | 0  1  1  1  1 0 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 0
.x .. .. ..    | 0  2 | *  * 12  *  *  * | 0  1  0  0  0 1 1 1 0 0 0 | 1 1 1 0 0 0 1 1 1 0 | 1 1 1 0 1
.. .x .. ..    | 0  2 | *  *  * 12  *  * | 0  0  1  0  0 1 0 0 1 1 0 | 1 0 0 1 1 0 1 1 0 1 | 1 1 0 1 1
.. .. .x ..    | 0  2 | *  *  *  * 12  * | 0  0  0  1  0 0 1 0 1 0 1 | 0 1 0 1 0 1 1 0 1 1 | 1 0 1 1 1
.. .. .. .x    | 0  2 | *  *  *  *  * 12 | 0  0  0  0  1 0 0 1 0 1 1 | 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1
---------------+------+------------------+---------------------------+---------------------+----------
.. .. o.3x.    | 3  0 | 3  0  0  0  0  0 | 1  *  *  *  * * * * * * * | 0 0 0 0 0 4 0 0 0 0 | 0 0 2 2 0
ox .. .. ..&#x | 1  2 | 0  2  1  0  0  0 | * 12  *  *  * * * * * * * | 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0
.. ox .. ..&#x | 1  2 | 0  2  0  1  0  0 | *  * 12  *  * * * * * * * | 1 0 0 1 1 0 0 0 0 0 | 1 1 0 1 0
.. .. ox ..&#x | 1  2 | 0  2  0  0  1  0 | *  *  * 12  * * * * * * * | 0 1 0 1 0 1 0 0 0 0 | 1 0 1 1 0
.. .. .. xx&#x | 2  2 | 1  2  0  0  0  1 | *  *  *  * 12 * * * * * * | 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0
.x .x .. ..    | 0  4 | 0  0  2  2  0  0 | *  *  *  *  * 6 * * * * * | 1 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1
.x .. .x ..    | 0  4 | 0  0  2  0  2  0 | *  *  *  *  * * 6 * * * * | 0 1 0 0 0 0 1 0 1 0 | 1 0 1 0 1
.x .. .. .x    | 0  4 | 0  0  2  0  0  2 | *  *  *  *  * * * 6 * * * | 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1
.. .x .x ..    | 0  4 | 0  0  0  2  2  0 | *  *  *  *  * * * * 6 * * | 0 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1
.. .x .. .x    | 0  4 | 0  0  0  2  0  2 | *  *  *  *  * * * * * 6 * | 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1
.. .. .x3.x    | 0  6 | 0  0  0  0  3  3 | *  *  *  *  * * * * * * 4 | 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1
---------------+------+------------------+---------------------------+---------------------+----------
ox ox .. ..&#x ♦ 1  4 | 0  4  2  2  0  0 | 0  2  2  0  0 1 0 0 0 0 0 | 6 * * * * * * * * * | 1 1 0 0 0
ox .. ox ..&#x ♦ 1  4 | 0  4  2  0  2  0 | 0  2  0  2  0 0 1 0 0 0 0 | * 6 * * * * * * * * | 1 0 1 0 0
ox .. .. xx&#x ♦ 2  4 | 1  4  2  0  0  2 | 0  2  0  0  2 0 0 1 0 0 0 | * * 6 * * * * * * * | 0 1 1 0 0
.. ox ox ..&#x ♦ 1  4 | 0  4  0  2  2  0 | 0  0  2  2  0 0 0 0 1 0 0 | * * * 6 * * * * * * | 1 0 0 1 0
.. ox .. xx&#x ♦ 2  4 | 1  4  0  2  0  2 | 0  0  2  0  2 0 0 0 0 1 0 | * * * * 6 * * * * * | 0 1 0 1 0
.. .. ox3xx&#x ♦ 3  6 | 3  6  0  0  3  3 | 1  0  0  3  3 0 0 0 0 0 1 | * * * * * 4 * * * * | 0 0 1 1 0
.x .x .x ..    ♦ 0  8 | 0  0  4  4  4  0 | 0  0  0  0  0 2 2 0 2 0 0 | * * * * * * 3 * * * | 1 0 0 0 1
.x .x .. .x    ♦ 0  8 | 0  0  4  4  0  4 | 0  0  0  0  0 2 0 2 0 2 0 | * * * * * * * 3 * * | 0 1 0 0 1
.x .. .x3.x    ♦ 0 12 | 0  0  6  0  6  6 | 0  0  0  0  0 0 3 3 0 0 2 | * * * * * * * * 2 * | 0 0 1 0 1
.. .x .x3.x    ♦ 0 12 | 0  0  0  6  6  6 | 0  0  0  0  0 0 0 0 3 3 2 | * * * * * * * * * 2 | 0 0 0 1 1
---------------+------+------------------+---------------------------+---------------------+----------
ox ox ox ..&#x ♦ 1  8 | 0  8  4  4  4  0 | 0  4  4  4  0 2 2 0 2 0 0 | 2 2 0 2 0 0 1 0 0 0 | 3 * * * *
ox ox .. xx&#x ♦ 2  8 | 1  8  4  4  0  4 | 0  4  4  0  4 2 0 2 0 2 0 | 2 0 2 0 2 0 0 1 0 0 | * 3 * * *
ox .. ox3xx&#x ♦ 3 12 | 3 12  6  0  6  6 | 1  6  0  6  6 0 3 3 0 0 2 | 0 3 3 0 0 2 0 0 1 0 | * * 2 * *
.. ox ox3xx&#x ♦ 3 12 | 3 12  0  6  6  6 | 1  0  6  6  6 0 0 0 3 3 2 | 0 0 0 3 3 2 0 0 0 1 | * * * 2 *
.x .x .x3.x    ♦ 0 24 | 0  0 12 12 12 12 | 0  0  0  0  0 6 6 6 6 6 4 | 0 0 0 0 0 0 3 3 2 2 | * * * * 1

oxx oxx3xxx&#x   → height(1,2) = height(1,3) = sqrt(5/12) = 0.645497
                   height(2,3) = 1
                   height(1,23) = 1/sqrt(6) = 0.408248 ({3} || shiddip)

o.. o..3o..    | 3  *  * | 2  4  4 0 0 0  0 0 0 0 | 1 2 2 4  4 2 2 4 0 0 0 0 0 0 0 0 0 | 1 2 2 2 2 4 1 2 2 0 0 0 0 0 | 1 1 2 2 1 0
.o. .o.3.o.    | * 12  * | 0  1  0 1 1 1  1 0 0 0 | 0 1 1 1  1 0 0 0 1 1 1 1 1 1 0 0 0 | 1 1 1 1 1 1 0 0 0 1 1 1 1 0 | 1 1 1 1 0 1
..o ..o3..o    | *  * 12 | 0  0  1 0 0 0  1 1 1 1 | 0 0 0 0  1 1 1 1 0 0 0 1 1 1 1 1 1 | 0 0 0 1 1 1 1 1 1 0 1 1 1 1 | 0 1 1 1 1 1
---------------+---------+------------------------+------------------------------------+-----------------------------+------------
... ... x..    | 2  0  0 | 3  *  * * * *  * * * * | 1 0 0 2  0 0 0 2 0 0 0 0 0 0 0 0 0 | 0 1 2 0 0 2 0 1 2 0 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 0 0 0 | 1 1 1 1 1 1 0 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 | 0 0 0 1 1 1 1 1 1 0 0 0 0 0 | 0 1 1 1 1 0
.x. ... ...    | 0  2  0 | *  *  * 6 * *  * * * * | 0 1 0 0  0 0 0 0 1 1 0 1 0 0 0 0 0 | 1 1 0 1 0 0 0 0 0 1 1 1 0 0 | 1 1 1 0 0 1
... .x. ...    | 0  2  0 | *  *  * * 6 *  * * * * | 0 0 1 0  0 0 0 0 1 0 1 0 1 0 0 0 0 | 1 0 1 0 1 0 0 0 0 1 1 0 1 0 | 1 1 0 1 0 1
... ... .x.    | 0  2  0 | *  *  * * * 6  * * * * | 0 0 0 1  0 0 0 0 0 1 1 0 0 1 0 0 0 | 0 1 1 0 0 1 0 0 0 1 0 1 1 0 | 1 0 1 1 0 1
.oo .oo3.oo&#x | 0  1  1 | *  *  * * * * 12 * * * | 0 0 0 0  1 0 0 0 0 0 0 1 1 1 0 0 0 | 0 0 0 1 1 1 0 0 0 0 1 1 1 0 | 0 1 1 1 0 1
..x ... ...    | 0  0  2 | *  *  * * * *  * 6 * * | 0 0 0 0  0 1 0 0 0 0 0 1 0 0 1 1 0 | 0 0 0 1 0 0 1 1 0 0 1 1 0 1 | 0 1 1 0 1 1
... ..x ...    | 0  0  2 | *  *  * * * *  * * 6 * | 0 0 0 0  0 0 1 0 0 0 0 0 1 0 1 0 1 | 0 0 0 0 1 0 1 0 1 0 1 0 1 1 | 0 1 0 1 1 1
... ... ..x    | 0  0  2 | *  *  * * * *  * * * 6 | 0 0 0 0  0 0 0 1 0 0 0 0 0 1 0 1 1 | 0 0 0 0 0 1 0 1 1 0 0 1 1 1 | 0 0 1 1 1 1
---------------+---------+------------------------+------------------------------------+-----------------------------+------------
... o..3x..    | 3  0  0 | 3  0  0 0 0 0  0 0 0 0 | 1 * * *  * * * * * * * * * * * * * | 0 0 2 0 0 0 0 0 2 0 0 0 0 0 | 1 0 0 2 1 0
ox. ... ...&#x | 1  2  0 | 0  2  0 1 0 0  0 0 0 0 | * 6 * *  * * * * * * * * * * * * * | 1 1 0 1 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
... ox. ...&#x | 1  2  0 | 0  2  0 0 1 0  0 0 0 0 | * * 6 *  * * * * * * * * * * * * * | 1 0 1 0 1 0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0
... ... xx.&#x | 2  2  0 | 1  2  0 0 0 1  0 0 0 0 | * * * 6  * * * * * * * * * * * * * | 0 1 1 0 0 1 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0
ooo ooo3ooo&#x | 1  1  1 | 0  1  1 0 0 0  1 0 0 0 | * * * * 12 * * * * * * * * * * * * | 0 0 0 1 1 1 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0
o.x ... ...&#x | 1  0  2 | 0  0  2 0 0 0  0 1 0 0 | * * * *  * 6 * * * * * * * * * * * | 0 0 0 1 0 0 1 1 0 0 0 0 0 0 | 0 1 1 0 1 0
... o.x ...&#x | 1  0  2 | 0  0  2 0 0 0  0 0 1 0 | * * * *  * * 6 * * * * * * * * * * | 0 0 0 0 1 0 1 0 1 0 0 0 0 0 | 0 1 0 1 1 0
... ... x.x&#x | 2  0  2 | 1  0  2 0 0 0  0 0 0 1 | * * * *  * * * 6 * * * * * * * * * | 0 0 0 0 0 1 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0
.x. .x. ...    | 0  4  0 | 0  0  0 2 2 0  0 0 0 0 | * * * *  * * * * 3 * * * * * * * * | 1 0 0 0 0 0 0 0 0 1 1 0 0 0 | 1 1 0 0 0 1
.x. ... .x.    | 0  4  0 | 0  0  0 2 0 2  0 0 0 0 | * * * *  * * * * * 3 * * * * * * * | 0 1 0 0 0 0 0 0 0 1 0 1 0 0 | 1 0 1 0 0 1
... .x.3.x.    | 0  6  0 | 0  0  0 0 3 3  0 0 0 0 | * * * *  * * * * * * 2 * * * * * * | 0 0 1 0 0 0 0 0 0 1 0 0 1 0 | 1 0 0 1 0 1
.xx ... ...&#x | 0  2  2 | 0  0  0 1 0 0  2 1 0 0 | * * * *  * * * * * * * 6 * * * * * | 0 0 0 1 0 0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
... .xx ...&#x | 0  2  2 | 0  0  0 0 1 0  2 0 1 0 | * * * *  * * * * * * * * 6 * * * * | 0 0 0 0 1 0 0 0 0 0 1 0 1 0 | 0 1 0 1 0 1
... ... .xx&#x | 0  2  2 | 0  0  0 0 0 1  2 0 0 1 | * * * *  * * * * * * * * * 6 * * * | 0 0 0 0 0 1 0 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 0 | * * * *  * * * * * * * * * * 3 * * | 0 0 0 0 0 0 1 0 0 0 1 0 0 1 | 0 1 0 0 1 1
..x ... ..x    | 0  0  4 | 0  0  0 0 0 0  0 2 0 2 | * * * *  * * * * * * * * * * * 3 * | 0 0 0 0 0 0 0 1 0 0 0 1 0 1 | 0 0 1 0 1 1
... ..x3..x    | 0  0  6 | 0  0  0 0 0 0  0 0 3 3 | * * * *  * * * * * * * * * * * * 2 | 0 0 0 0 0 0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
---------------+---------+------------------------+------------------------------------+-----------------------------+------------
ox. ox. ...&#x ♦ 1  4  0 | 0  4  0 2 2 0  0 0 0 0 | 0 2 2 0  0 0 0 0 1 0 0 0 0 0 0 0 0 | 3 * * * * * * * * * * * * * | 1 1 0 0 0 0
ox. ... xx.&#x ♦ 2  4  0 | 1  4  0 2 0 2  0 0 0 0 | 0 2 0 2  0 0 0 0 0 1 0 0 0 0 0 0 0 | * 3 * * * * * * * * * * * * | 1 0 1 0 0 0
... ox.3xx.&#x ♦ 3  6  0 | 3  6  0 0 3 3  0 0 0 0 | 1 0 3 3  0 0 0 0 0 0 1 0 0 0 0 0 0 | * * 2 * * * * * * * * * * * | 1 0 0 1 0 0
oxx ... ...&#x ♦ 1  2  2 | 0  2  2 1 0 0  2 1 0 0 | 0 1 0 0  2 1 0 0 0 0 0 1 0 0 0 0 0 | * * * 6 * * * * * * * * * * | 0 1 1 0 0 0
... oxx ...&#x ♦ 1  2  2 | 0  2  2 0 1 0  2 0 1 0 | 0 0 1 0  2 0 1 0 0 0 0 0 1 0 0 0 0 | * * * * 6 * * * * * * * * * | 0 1 0 1 0 0
... ... xxx&#x ♦ 2  2  2 | 1  2  2 0 0 1  2 0 0 1 | 0 0 0 1  2 0 0 1 0 0 0 0 0 1 0 0 0 | * * * * * 6 * * * * * * * * | 0 0 1 1 0 0
o.x o.x ...&#x ♦ 1  0  4 | 0  0  4 0 0 0  0 2 2 0 | 0 0 0 0  0 2 2 0 0 0 0 0 0 0 1 0 0 | * * * * * * 3 * * * * * * * | 0 1 0 0 1 0
o.x ... x.x&#x ♦ 2  0  4 | 1  0  4 0 0 0  0 2 0 2 | 0 0 0 0  0 2 0 2 0 0 0 0 0 0 0 1 0 | * * * * * * * 3 * * * * * * | 0 0 1 0 1 0
... o.x3x.x&#x ♦ 3  0  6 | 3  0  6 0 0 0  0 0 3 3 | 1 0 0 0  0 0 3 3 0 0 0 0 0 0 0 0 1 | * * * * * * * * 2 * * * * * | 0 0 0 1 1 0
.x. .x.3.x.    ♦ 0 12  0 | 0  0  0 6 6 6  0 0 0 0 | 0 0 0 0  0 0 0 0 3 3 2 0 0 0 0 0 0 | * * * * * * * * * 1 * * * * | 1 0 0 0 0 1
.xx .xx ...&#x ♦ 0  4  4 | 0  0  0 2 2 0  4 2 2 0 | 0 0 0 0  0 0 0 0 1 0 0 2 2 0 1 0 0 | * * * * * * * * * * 3 * * * | 0 1 0 0 0 1
.xx ... .xx&#x ♦ 0  4  4 | 0  0  0 2 0 2  4 2 0 2 | 0 0 0 0  0 0 0 0 0 1 0 2 0 2 0 1 0 | * * * * * * * * * * * 3 * * | 0 0 1 0 0 1
... .xx3.xx&#x ♦ 0  6  6 | 0  0  0 0 3 3  6 0 3 3 | 0 0 0 0  0 0 0 0 0 0 1 0 3 3 0 0 1 | * * * * * * * * * * * * 2 * | 0 0 0 1 0 1
..x ..x3..x    ♦ 0  0 12 | 0  0  0 0 0 0  0 6 6 6 | 0 0 0 0  0 0 0 0 0 0 0 0 0 0 3 3 2 | * * * * * * * * * * * * * 1 | 0 0 0 0 1 1
---------------+---------+------------------------+------------------------------------+-----------------------------+------------
ox. ox.3xx.&#x ♦ 3 12  0 | 3 12  0 6 6 6  0 0 0 0 | 1 6 6 6  0 0 0 0 3 3 2 0 0 0 0 0 0 | 3 3 2 0 0 0 0 0 0 1 0 0 0 0 | 1 * * * * *
oxx oxx ...&#x ♦ 1  4  4 | 0  4  4 2 2 0  4 2 2 0 | 0 2 2 0  4 2 2 0 1 0 0 2 2 0 1 0 0 | 1 0 0 2 2 0 1 0 0 0 1 0 0 0 | * 3 * * * *
oxx ... xxx&#x ♦ 2  4  4 | 1  4  4 2 0 2  4 2 0 2 | 0 2 0 2  4 2 0 2 0 1 0 2 0 2 0 1 0 | 0 1 0 2 0 2 0 1 0 0 0 1 0 0 | * * 3 * * *
... oxx3xxx&#x ♦ 3  6  6 | 3  6  6 0 3 3  6 0 3 3 | 1 0 3 3  6 0 3 3 0 0 1 0 3 3 0 0 1 | 0 0 1 0 3 3 0 0 1 0 0 0 1 0 | * * * 2 * *
o.x o.x3x.x&#x ♦ 3  0 12 | 3  0 12 0 0 0  0 6 6 6 | 1 0 0 0  0 6 6 6 0 0 0 0 0 0 3 3 2 | 0 0 0 0 0 0 3 3 2 0 0 0 0 1 | * * * * 1 *
.xx .xx3.xx&#x ♦ 0 12 12 | 0  0  0 6 6 6 12 6 6 6 | 0 0 0 0  0 0 0 0 3 3 2 6 6 6 3 3 2 | 0 0 0 0 0 0 0 0 0 1 3 3 2 1 | * * * * * 1