If one of the vertices of oct would be chopped off, this would result in the pyramid product of {3} with squippy. Then, asigning the remaining tip atop the square as one atop the triangle instead, one recognizes that diminishing to be nothing but squepe.

Incidence matrix according to Dynkin symbol

xo3oo ox3oo4oo&#x   → height = 1/sqrt(6) = 0.408248
(pyramid product of {3} with oct)

o.3o. o.3o.4o.    | 3 * ♦ 2  6  0 | 1 12 12 0 | 6 24  8 0 | 12 16 1 | 8 2
.o3.o .o3.o4.o    | * 6 ♦ 0  3  4 | 0  3 12 4 | 1 12 12 1 |  4 12 3 | 4 3
------------------+-----+---------+-----------+-----------+---------+----
x. .. .. .. ..    | 2 0 | 3  *  * ♦ 1  6  0 0 | 6 12  0 0 | 12  8 0 | 8 1
oo3oo oo3oo4oo&#x | 1 1 | * 18  * ♦ 0  2  4 0 | 1  8  4 0 |  4  8 1 | 4 2
.. .. .x .. ..    | 0 2 | *  * 12 | 0  0  3 2 | 0  3  6 1 |  1  6 3 | 2 3
------------------+-----+---------+-----------+-----------+---------+----
x.3o. .. .. ..    | 3 0 | 3  0  0 | 1  *  * * ♦ 6  0  0 0 | 12  0 0 | 8 0
xo .. .. .. ..&#x | 2 1 | 1  2  0 | * 18  * * ♦ 1  4  0 0 |  4  4 0 | 4 1
.. .. ox .. ..&#x | 1 2 | 0  2  1 | *  * 36 * | 0  2  2 0 |  1  4 1 | 2 2
.. .. .x3.o ..    | 0 3 | 0  0  3 | *  *  * 8 | 0  0  3 1 |  0  3 3 | 1 3
------------------+-----+---------+-----------+-----------+---------+----
xo3oo .. .. ..&#x ♦ 3 1 | 3  3  0 | 1  3  0 0 | 6  *  * * |  4  0 0 | 4 0
xo .. ox .. ..&#x ♦ 2 2 | 1  4  1 | 0  2  2 0 | * 36  * * |  1  2 0 | 2 1
.. .. ox3oo ..&#x ♦ 1 3 | 0  3  3 | 0  0  3 1 | *  * 24 * |  0  2 1 | 1 2
.. .. .x3.o4.o    ♦ 0 6 | 0  0 12 | 0  0  0 8 | *  *  * 1 |  0  0 3 | 0 3
------------------+-----+---------+-----------+-----------+---------+----
xo3oo ox .. ..&#x ♦ 3 2 | 3  6  1 | 1  6  3 0 | 2  3  0 0 | 12  * * | 2 0
xo .. ox3oo ..&#x ♦ 2 3 | 1  6  3 | 0  3  6 1 | 0  3  2 0 |  * 24 * | 1 1
.. .. ox3oo4oo&#x ♦ 1 6 | 0  6 12 | 0  0 12 8 | 0  0  8 1 |  *  * 3 | 0 2
------------------+-----+---------+-----------+-----------+---------+----
xo3oo ox3oo ..&#x ♦ 3 3 | 3  9  3 | 1  9  9 1 | 3  9  3 0 |  3  3 0 | 8 *
xo .. ox3oo4oo&#x ♦ 2 6 | 1 12 12 | 0  6 24 8 | 0 12 16 1 |  0  8 2 | * 3

xo3oo oo3ox3oo&#x   → height = 1/sqrt(6) = 0.408248
(pyramid product of {3} with oct)

o.3o. o.3o.3o.    | 3 * ♦ 2  6  0 | 1 12 12 0 0 | 6 24  4  4 0 | 12  8  8 1 | 4 4 2
.o3.o .o3.o3.o    | * 6 ♦ 0  3  4 | 0  3 12 2 2 | 1 12  6  6 1 |  4  6  6 3 | 2 2 3
------------------+-----+---------+-------------+--------------+------------+------
x. .. .. .. ..    | 2 0 | 3  *  * ♦ 1  6  0 0 0 | 6 12  0  0 0 | 12  4  4 0 | 4 4 1
oo3oo oo3oo3oo&#x | 1 1 | * 18  * ♦ 0  2  4 0 0 | 1  8  2  2 0 |  4  4  4 1 | 2 2 2
.. .. .. .x ..    | 0 2 | *  * 12 | 0  0  3 1 1 | 0  3  3  3 1 |  1  3  3 3 | 1 1 3
------------------+-----+---------+-------------+--------------+------------+------
x.3o. .. .. ..    | 3 0 | 3  0  0 | 1  *  * * * ♦ 6  0  0  0 0 | 12  0  0 0 | 4 4 0
xo .. .. .. ..&#x | 2 1 | 1  2  0 | * 18  * * * ♦ 1  4  0  0 0 |  4  2  2 0 | 2 2 1
.. .. .. ox ..&#x | 1 2 | 0  2  1 | *  * 36 * * | 0  2  1  1 0 |  1  2  2 1 | 1 1 2
.. .. .o3.x ..    | 0 3 | 0  0  3 | *  *  * 4 * | 0  0  3  0 1 |  0  3  0 3 | 1 0 3
.. .. .. .x3.o    | 0 3 | 0  0  3 | *  *  * * 4 | 0  0  0  3 1 |  0  0  3 3 | 0 1 3
------------------+-----+---------+-------------+--------------+------------+------
xo3oo .. .. ..&#x ♦ 3 1 | 3  3  0 | 1  3  0 0 0 | 6  *  *  * * |  4  0  0 0 | 2 2 0
xo .. .. ox ..&#x ♦ 2 2 | 1  4  1 | 0  2  2 0 0 | * 36  *  * * |  1  1  1 0 | 1 1 1
.. .. oo3ox ..&#x ♦ 1 3 | 0  3  3 | 0  0  3 1 0 | *  * 12  * * |  0  2  0 1 | 1 0 2
.. .. .. ox3oo&#x ♦ 1 3 | 0  3  3 | 0  0  3 0 1 | *  *  * 12 * |  0  0  2 1 | 0 1 2
.. .. .o3.x3.o    ♦ 0 6 | 0  0 12 | 0  0  0 4 4 | *  *  *  * 1 |  0  0  0 3 | 0 0 3
------------------+-----+---------+-------------+--------------+------------+------
xo3oo .. ox ..&#x ♦ 3 2 | 3  6  1 | 1  6  3 0 0 | 2  3  0  0 0 | 12  *  * * | 1 1 0
xo .. oo3ox ..&#x ♦ 2 3 | 1  6  3 | 0  3  6 1 0 | 0  3  2  0 0 |  * 12  * * | 1 0 1
xo .. .. ox3oo&#x ♦ 2 3 | 1  6  3 | 0  3  6 0 1 | 0  3  0  2 0 |  *  * 12 * | 0 1 1
.. .. oo3ox3oo&#x ♦ 1 6 | 0  6 12 | 0  0 12 4 4 | 0  0  4  4 1 |  *  *  * 3 | 0 0 2
------------------+-----+---------+-------------+--------------+------------+------
xo3oo oo3ox ..&#x ♦ 3 3 | 3  9  3 | 1  9  9 1 0 | 3  9  3  0 0 |  3  3  0 0 | 4 * *
xo3oo .. ox3oo&#x ♦ 3 3 | 3  9  3 | 1  9  9 0 1 | 3  9  0  3 0 |  3  0  3 0 | * 4 *
xo .. oo3ox3oo&#x ♦ 2 6 | 1 12 12 | 0  6 24 4 4 | 0 12  8  8 1 |  0  4  4 2 | * * 3

xoo3oox oxo3ooo&#x   → height(1,2) = height(2,3) = 1/sqrt(3) = 0.577350
                       height(1,3) = sqrt(2/3) = 0.816497

o..3o.. o..3o..    | 3 * * ♦ 2 3 2 0 0 0 | 1 6 3 2 1  6 0 0 0 0 | 3 6 1 1 6 3  6 0 0 0 | 3 2 3 6 3 2 0 0 | 1 3 2 1 0
.o.3.o. .o.3.o.    | * 3 * ♦ 0 3 0 2 3 0 | 0 3 6 0 0  6 1 3 6 0 | 1 6 3 0 3 3 12 1 6 3 | 2 3 1 6 6 6 2 3 | 1 2 3 3 1
..o3..o ..o3..o    | * * 3 ♦ 0 0 2 0 3 2 | 0 0 0 1 2  6 0 6 3 1 | 0 0 0 1 3 6  6 3 6 1 | 0 0 3 3 6 2 3 2 | 0 3 1 2 1
-------------------+-------+-------------+----------------------+----------------------+-----------------+----------
x.. ... ... ...    | 2 0 0 | 3 * * * * * | 1 3 0 1 0  0 0 0 0 0 | 3 3 0 1 3 0  0 0 0 0 | 3 1 3 3 0 0 0 0 | 1 3 1 0 0
oo.3oo. oo.3oo.&#x | 1 1 0 | * 9 * * * * ♦ 0 2 2 0 0  2 0 0 0 0 | 1 4 1 0 2 1  4 0 0 0 | 2 2 1 4 2 2 0 0 | 1 2 2 1 0
o.o3o.o o.o3o.o&#x | 1 0 1 | * * 6 * * * | 0 0 0 1 1  3 0 0 0 0 | 0 0 0 1 3 3  3 0 0 0 | 0 0 3 3 3 1 0 0 | 0 3 1 1 0
... ... .x. ...    | 0 2 0 | * * * 3 * * ♦ 0 0 3 0 0  0 1 0 3 0 | 0 3 3 0 0 0  6 0 3 3 | 1 3 0 3 3 6 1 3 | 1 1 3 3 1
.oo3.oo .oo3.oo&#x | 0 1 1 | * * * * 9 * ♦ 0 0 0 0 0  2 0 2 2 0 | 0 0 0 0 1 2  4 1 4 1 | 0 0 1 2 4 2 2 2 | 0 2 1 2 1
... ..x ... ...    | 0 0 2 | * * * * * 3 | 0 0 0 0 1  0 0 3 0 1 | 0 0 0 1 0 3  0 3 3 0 | 0 0 3 0 3 0 3 1 | 0 3 0 1 1
-------------------+-------+-------------+----------------------+----------------------+-----------------+----------
x..3o.. ... ...    | 3 0 0 | 3 0 0 0 0 0 | 1 * * * *  * * * * * | 3 0 0 1 0 0  0 0 0 0 | 3 0 3 0 0 0 0 0 | 1 3 0 0 0
xo. ... ... ...&#x | 2 1 0 | 1 2 0 0 0 0 | * 9 * * *  * * * * * | 1 2 0 0 1 0  0 0 0 0 | 2 1 1 2 0 2 0 0 | 1 2 1 0 0
... ... ox. ...&#x | 1 2 0 | 0 2 0 1 0 0 | * * 9 * *  * * * * * ♦ 0 2 1 0 0 0  1 0 0 0 | 1 2 0 2 1 2 0 0 | 1 1 2 1 0
x.o ... ... ...&#x | 2 0 1 | 1 0 2 0 0 0 | * * * 3 *  * * * * * | 0 0 0 1 3 0  0 0 0 0 | 0 0 3 3 0 0 0 0 | 0 3 1 0 0
... o.x ... ...&#x | 1 0 2 | 0 0 2 0 0 1 | * * * * 3  * * * * * | 0 0 0 1 0 3  0 0 0 0 | 0 0 3 0 3 0 0 0 | 0 3 0 1 0
ooo3ooo ooo3ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * * * 18 * * * * | 0 0 0 0 1 1  2 0 0 0 | 0 0 1 2 2 1 0 0 | 0 2 1 1 0
... ... .x.3.o.    | 0 3 0 | 0 0 0 3 0 0 | * * * * *  * 1 * * * ♦ 0 0 3 0 0 0  0 0 0 3 | 0 3 0 0 0 6 0 3 | 1 0 3 3 1
... .ox ... ...&#x | 0 1 2 | 0 0 0 0 2 1 | * * * * *  * * 9 * * | 0 0 0 0 0 1  0 1 2 0 | 0 0 1 0 2 0 2 1 | 0 2 0 1 1
... ... .xo ...&#x | 0 2 1 | 0 0 0 1 2 0 | * * * * *  * * * 9 * ♦ 0 0 0 0 0 0  2 0 2 1 | 0 0 0 1 2 2 1 2 | 0 1 1 2 1
..o3..x ... ...    | 0 0 3 | 0 0 0 0 0 3 | * * * * *  * * * * 1 | 0 0 0 1 0 0  0 3 0 0 | 0 0 3 0 0 0 3 0 | 0 3 0 0 1
-------------------+-------+-------------+----------------------+----------------------+-----------------+----------
xo.3oo. ... ...&#x ♦ 3 1 0 | 3 3 0 0 0 0 | 1 3 0 0 0  0 0 0 0 0 | 3 * * * * *  * * * * | 2 0 1 0 0 0 0 0 | 1 2 0 0 0
xo. ... ox. ...&#x ♦ 2 2 0 | 1 4 0 1 0 0 | 0 2 2 0 0  0 0 0 0 0 | * 9 * * * *  * * * * | 1 1 0 1 0 0 0 0 | 1 1 1 0 0
... ... ox.3oo.&#x ♦ 1 3 0 | 0 3 0 3 0 0 | 0 0 3 0 0  0 1 0 0 0 | * * 3 * * *  * * * * | 0 2 0 0 0 2 0 0 | 1 0 2 1 0
x.o3o.x ... ...&#x ♦ 3 0 3 | 3 0 6 0 0 3 | 1 0 0 3 3  0 0 0 0 1 | * * * 1 * *  * * * * | 0 0 3 0 0 0 0 0 | 0 3 0 0 0
xoo ... ... ...&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 0 1 0 1 0  2 0 0 0 0 | * * * * 9 *  * * * * | 0 0 1 2 0 0 0 0 | 0 2 1 0 0
... oox ... ...&#x ♦ 1 1 2 | 0 1 2 0 2 1 | 0 0 0 0 1  2 0 1 0 0 | * * * * * 9  * * * * | 0 0 1 0 2 0 0 0 | 0 2 0 1 0
... ... oxo ...&#x ♦ 1 2 1 | 0 2 1 1 2 0 | 0 0 1 0 0  2 0 0 1 0 | * * * * * * 18 * * * | 0 0 0 1 1 1 0 0 | 0 1 1 1 0
.oo3.ox ... ...&#x ♦ 0 1 3 | 0 0 0 0 3 3 | 0 0 0 0 0  0 0 3 0 1 | * * * * * *  * 3 * * | 0 0 1 0 0 0 2 0 | 0 2 0 0 1
... .ox .xo ...&#x ♦ 0 2 2 | 0 0 0 1 4 1 | 0 0 0 0 0  0 0 2 2 0 | * * * * * *  * * 9 * | 0 0 0 0 1 0 1 1 | 0 1 0 1 1
... ... .xo3.oo&#x ♦ 0 3 1 | 0 0 0 3 3 0 | 0 0 0 0 0  0 1 0 3 0 | * * * * * *  * * * 3 | 0 0 0 0 0 2 0 2 | 0 0 1 2 1
-------------------+-------+-------------+----------------------+----------------------+-----------------+----------
xo.3oo. ox. ...&#x ♦ 3 2 0 | 3 6 0 1 0 0 | 1 6 3 0 0  0 0 0 0 0 | 2 3 0 0 0 0  0 0 0 0 | 3 * * * * * * * | 1 1 0 0 0
xo. ... ox.3oo.&#x ♦ 2 3 0 | 1 6 0 3 0 0 | 0 3 6 0 0  0 1 0 0 0 | 0 3 2 0 0 0  0 0 0 0 | * 3 * * * * * * | 1 0 1 0 0
xoo3oox ... ...&#x ♦ 3 1 3 | 3 3 6 0 3 3 | 1 3 0 3 3  6 0 3 0 1 | 1 0 0 1 3 3  0 1 0 0 | * * 3 * * * * * | 0 2 0 0 0
xoo ... oxo ...&#x ♦ 2 2 1 | 1 4 2 1 2 0 | 0 2 2 1 0  4 0 0 1 0 | 0 1 0 0 2 0  2 0 0 0 | * * * 9 * * * * | 0 1 1 0 0
... oox oxo ...&#x ♦ 1 2 2 | 0 2 2 1 4 1 | 0 0 1 0 1  4 0 2 2 0 | 0 0 0 0 0 2  2 0 1 0 | * * * * 9 * * * | 0 1 0 1 0
... ... oxo3ooo&#x ♦ 1 3 1 | 0 3 1 3 3 0 | 0 0 3 0 0  3 1 0 3 0 | 0 0 1 0 0 0  3 0 0 1 | * * * * * 6 * * | 0 0 1 1 0
.oo3.ox .xo ...&#x ♦ 0 2 3 | 0 0 0 1 6 3 | 0 0 0 0 0  0 0 6 3 1 | 0 0 0 0 0 0  0 2 3 0 | * * * * * * 3 * | 0 1 0 0 1
... .ox .xo3.oo&#x ♦ 0 3 2 | 0 0 0 3 6 1 | 0 0 0 0 0  0 1 3 6 0 | 0 0 0 0 0 0  0 0 3 2 | * * * * * * * 3 | 0 0 0 1 1
-------------------+-------+-------------+----------------------+----------------------+-----------------+----------
xo.3oo. ox.3oo.&#x ♦ 3 3 0 | 3 9 0 3 0 0 | 1 9 9 0 0  0 1 0 0 0 | 3 9 3 0 0 0  0 0 0 0 | 3 3 0 0 0 0 0 0 | 1 * * * *
xoo3oox oxo ...&#x ♦ 3 2 3 | 3 6 6 1 6 3 | 1 6 3 3 3 12 0 6 3 1 | 2 3 0 1 6 6  6 2 3 0 | 1 0 2 3 3 0 1 0 | * 3 * * *
xoo ... oxo3ooo&#x ♦ 2 3 1 | 1 6 2 3 3 0 | 0 3 6 1 0  6 1 0 3 0 | 0 3 2 0 3 0  6 0 0 1 | 0 1 0 3 0 2 0 0 | * * 3 * *
... oox oxo3ooo&#x ♦ 1 3 2 | 0 3 2 3 6 1 | 0 0 3 0 1  6 1 3 6 0 | 0 0 1 0 0 3  6 0 3 2 | 0 0 0 0 3 2 0 1 | * * * 3 *
.oo3.ox .xo3.oo&#x ♦ 0 3 3 | 0 0 0 3 9 3 | 0 0 0 0 0  0 1 9 9 1 | 0 0 0 0 0 0  0 3 9 3 | 0 0 0 0 0 0 3 3 | * * * * 1

xoo oox3ooo4ooo&#x   → height(1,2) = sqrt(3)/2 = 0.866025
                       height(1,3) = 1/2
                       height(2,3) = 1/sqrt(2) = 0.707107

o.. o..3o..4o..    | 2 * * ♦ 1 1  6 0  0 | 1 3 12  6  0 0 | 12  8 6 12 0 0 | 8 1 12  8 0 | 1 8 1
.o. .o.3.o.4.o.    | * 1 * ♦ 0 2  0 6  0 | 1 0  0 12 12 0 |  0  0 6 24 8 0 | 0 0 12 16 1 | 0 8 2
..o ..o3..o4..o    | * * 6 ♦ 0 0  2 1  4 | 0 1  8  2  4 4 |  4  8 1  8 4 1 | 4 2  4  8 1 | 1 4 2
-------------------+-------+-------------+----------------+----------------+-------------+------
x.. ... ... ...    | 2 0 0 | 1 *  * *  * ♦ 1 6  0  0  0 0 | 12  0 6  0 0 0 | 8 0 12  0 0 | 1 8 0
oo. oo.3oo.4oo.&#x | 1 1 0 | * 2  * *  * ♦ 1 0  0  6  0 0 |  0  0 6 12 0 0 | 0 0 12  8 0 | 0 8 1
o.o o.o3o.o4o.o&#x | 1 0 1 | * * 12 *  * ♦ 0 1  4  1  0 0 |  4  4 1  4 0 0 | 4 1  4  4 0 | 1 4 1
.oo .oo3.oo4.oo&#x | 0 1 1 | * *  * 6  * ♦ 0 0  0  2  4 0 |  0  0 1  8 4 0 | 0 0  4  8 1 | 0 4 2
... ..x ... ...    | 0 0 2 | * *  * * 12 | 0 0  2  0  1 2 |  1  4 0  2 2 1 | 2 2  1  4 1 | 1 2 2
-------------------+-------+-------------+----------------+----------------+-------------+------
xo. ... ... ...&#x | 2 1 0 | 1 2  0 0  0 | 1 *  *  *  * * ♦  0  0 6  0 0 0 | 0 0 12  0 0 | 0 8 0
x.o ... ... ...&#x | 2 0 1 | 1 0  2 0  0 | * 6  *  *  * * ♦  4  0 1  0 0 0 | 4 0  4  0 0 | 1 4 0
... o.x ... ...&#x | 1 0 2 | 0 0  2 0  1 | * * 24  *  * * |  1  2 0  1 0 0 | 2 1  1  2 0 | 1 2 1
ooo ooo3ooo4ooo&#x | 1 1 1 | 0 1  1 1  0 | * *  * 12  * * ♦  0  0 1  4 0 0 | 0 0  4  4 0 | 0 4 1
... .ox ... ...&#x | 0 1 2 | 0 0  0 2  1 | * *  *  * 12 * |  0  0 0  2 2 0 | 0 0  1  4 1 | 0 2 2
... ..x3..o ...    | 0 0 3 | 0 0  0 0  3 | * *  *  *  * 8 |  0  2 0  0 1 1 | 1 2  0  2 1 | 1 1 2
-------------------+-------+-------------+----------------+----------------+-------------+------
x.o o.x ... ...&#x ♦ 2 0 2 | 1 0  4 0  1 | 0 2  2  0  0 0 | 12  * *  * * * | 2 0  1  0 0 | 1 2 0
... o.x3o.o ...&#x ♦ 1 0 3 | 0 0  3 0  3 | 0 0  3  0  0 1 |  * 16 *  * * * | 1 1  0  1 0 | 1 1 1
xoo ... ... ...&#x ♦ 2 1 1 | 1 2  2 1  0 | 1 1  0  2  0 0 |  *  * 6  * * * | 0 0  4  0 0 | 0 4 0
... oox ... ...&#x ♦ 1 1 2 | 0 1  2 2  1 | 0 0  1  2  1 0 |  *  * * 24 * * | 0 0  1  2 0 | 0 2 1
... .ox3.oo ...&#x ♦ 0 1 3 | 0 0  0 3  3 | 0 0  0  0  3 1 |  *  * *  * 8 * | 0 0  0  2 1 | 0 1 2
... ..x3..o4..o    ♦ 0 0 6 | 0 0  0 0 12 | 0 0  0  0  0 8 |  *  * *  * * 1 | 0 2  0  0 1 | 1 0 2
-------------------+-------+-------------+----------------+----------------+-------------+------
x.o o.x3o.o ...&#x ♦ 2 0 3 | 1 0  6 0  3 | 0 3  6  0  0 1 |  3  2 0  0 0 0 | 8 *  *  * * | 1 1 0
... o.x3o.o4o.o&#x ♦ 1 0 6 | 0 0  6 0 12 | 0 0 12  0  0 8 |  0  8 0  0 0 1 | * 2  *  * * | 1 0 1
xoo oox ... ...&#x ♦ 2 1 2 | 1 2  4 2  1 | 1 2  2  4  1 0 |  1  0 2  2 0 0 | * * 12  * * | 0 2 0
... oox3ooo ...&#x ♦ 1 1 3 | 0 1  3 3  3 | 0 0  3  3  3 1 |  0  1 0  3 1 0 | * *  * 16 * | 0 1 1
... .ox3.oo4.oo&#x ♦ 0 1 6 | 0 0  0 6 12 | 0 0  0  0 12 8 |  0  0 0  0 8 1 | * *  *  * 1 | 0 0 2
-------------------+-------+-------------+----------------+----------------+-------------+------
x.o o.x3o.o4o.o&#x ♦ 2 0 6 | 1 0 12 0 12 | 0 6 24  0  0 8 | 12 16 0  0 0 1 | 8 2  0  0 0 | 1 * *
xoo oox3ooo ...&#x ♦ 2 1 3 | 1 2  6 3  3 | 1 3  6  6  3 1 |  3  2 3  6 1 0 | 1 0  3  2 0 | * 8 *
... oox3ooo4ooo&#x ♦ 1 1 6 | 0 1  6 6 12 | 0 0 12  6 12 8 |  0  8 0 12 8 1 | 0 1  0  8 1 | * * 2

xoo ooo3oox3ooo&#x   → height(1,2) = sqrt(3)/2 = 0.866025
                       height(1,3) = 1/2
                       height(2,3) = 1/sqrt(2) = 0.707107

o.. o..3o..3o..    | 2 * * ♦ 1 1  6 0  0 | 1 3 12  6  0 0 0 | 12 4 4 6 12 0 0 0 | 4 4 1 12 4 4 0 | 1 4 4 1
.o. .o.3.o.3.o.    | * 1 * ♦ 0 2  0 6  0 | 1 0  0 12 12 0 0 |  0 0 0 6 24 4 4 0 | 0 0 0 12 8 8 1 | 0 4 4 2
..o ..o3..o3..o    | * * 6 ♦ 0 0  2 1  4 | 0 1  8  2  4 2 2 |  4 4 4 1  8 2 2 1 | 2 2 2  4 4 4 1 | 1 2 2 2
-------------------+-------+-------------+------------------+-------------------+----------------+--------
x.. ... ... ...    | 2 0 0 | 1 *  * *  * ♦ 1 6  0  0  0 0 0 | 12 0 0 6  0 0 0 0 | 4 4 0 12 0 0 0 | 1 4 4 0
oo. oo.3oo.3oo.&#x | 1 1 0 | * 2  * *  * ♦ 1 0  0  6  0 0 0 |  0 0 0 6 12 0 0 0 | 0 0 0 12 4 4 0 | 0 4 4 1
o.o o.o3o.o3o.o&#x | 1 0 1 | * * 12 *  * ♦ 0 1  4  1  0 0 0 |  4 2 2 1  4 0 0 0 | 2 2 1  4 2 2 0 | 1 2 2 1
.oo .oo3.oo3.oo&#x | 0 1 1 | * *  * 6  * ♦ 0 0  0  2  4 0 0 |  0 0 0 1  8 2 2 0 | 0 0 0  4 4 4 1 | 0 2 2 2
... ... ..x ...    | 0 0 2 | * *  * * 12 | 0 0  2  0  1 1 1 |  1 2 2 0  2 1 1 1 | 1 1 2  1 2 2 1 | 1 1 1 2
-------------------+-------+-------------+------------------+-------------------+----------------+--------
xo. ... ... ...&#x | 2 1 0 | 1 2  0 0  0 | 1 *  *  *  * * * ♦  0 0 0 6  0 0 0 0 | 0 0 0 12 0 0 0 | 0 4 4 0
x.o ... ... ...&#x | 2 0 1 | 1 0  2 0  0 | * 6  *  *  * * * ♦  4 0 0 1  0 0 0 0 | 2 2 0  4 0 0 0 | 1 2 2 0
... ... o.x ...&#x | 1 0 2 | 0 0  2 0  1 | * * 24  *  * * * |  1 1 1 0  1 0 0 0 | 1 1 1  1 1 1 0 | 1 1 1 1
ooo ooo3ooo3ooo&#x | 1 1 1 | 0 1  1 1  0 | * *  * 12  * * * ♦  0 0 0 1  4 0 0 0 | 0 0 0  4 2 2 0 | 0 2 2 1
... ... .ox ...&#x | 0 1 2 | 0 0  0 2  1 | * *  *  * 12 * * |  0 0 0 0  2 1 1 0 | 0 0 0  1 2 2 1 | 0 1 1 2
... ..o3..x ...    | 0 0 3 | 0 0  0 0  3 | * *  *  *  * 4 * |  0 2 0 0  0 1 0 1 | 1 0 2  0 2 0 1 | 1 1 0 2
... ... ..x3..o    | 0 0 3 | 0 0  0 0  3 | * *  *  *  * * 4 |  0 0 2 0  0 0 1 1 | 0 1 2  0 0 2 1 | 1 0 1 2
-------------------+-------+-------------+------------------+-------------------+----------------+--------
x.o ... o.x ...&#x ♦ 2 0 2 | 1 0  4 0  1 | 0 2  2  0  0 0 0 | 12 * * *  * * * * | 1 1 0  1 0 0 0 | 1 1 1 0
... o.o3o.x ...&#x ♦ 1 0 3 | 0 0  3 0  3 | 0 0  3  0  0 1 0 |  * 8 * *  * * * * | 1 0 1  0 1 0 0 | 1 1 0 1
... ... o.x3o.o&#x ♦ 1 0 3 | 0 0  3 0  3 | 0 0  3  0  0 0 1 |  * * 8 *  * * * * | 0 1 1  0 0 1 0 | 1 0 1 1
xoo ... ... ...&#x ♦ 2 1 1 | 1 2  2 1  0 | 1 1  0  2  0 0 0 |  * * * 6  * * * * | 0 0 0  4 0 0 0 | 0 2 2 0
... ... oox ...&#x ♦ 1 1 2 | 0 1  2 2  1 | 0 0  1  2  1 0 0 |  * * * * 24 * * * | 0 0 0  1 1 1 0 | 0 1 1 1
... .oo3.ox ...&#x ♦ 0 1 3 | 0 0  0 3  3 | 0 0  0  0  3 1 0 |  * * * *  * 4 * * | 0 0 0  0 2 0 1 | 0 1 0 2
... ... .ox3.oo&#x ♦ 0 1 3 | 0 0  0 3  3 | 0 0  0  0  3 0 1 |  * * * *  * * 4 * | 0 0 0  0 0 2 1 | 0 0 1 2
... ..o3..x3..o    ♦ 0 0 6 | 0 0  0 0 12 | 0 0  0  0  0 4 4 |  * * * *  * * * 1 | 0 0 2  0 0 0 1 | 1 0 0 2
-------------------+-------+-------------+------------------+-------------------+----------------+--------
x.o o.o3o.x ...&#x ♦ 2 0 3 | 1 0  6 0  3 | 0 3  6  0  0 1 0 |  3 2 0 0  0 0 0 0 | 4 * *  * * * * | 1 1 0 0
x.o ... o.x3o.o&#x ♦ 2 0 3 | 1 0  6 0  3 | 0 3  6  0  0 0 1 |  3 0 2 0  0 0 0 0 | * 4 *  * * * * | 1 0 1 0
... o.o3o.x3o.o&#x ♦ 1 0 6 | 0 0  6 0 12 | 0 0 12  0  0 4 4 |  0 4 4 0  0 0 0 1 | * * 2  * * * * | 1 0 0 1
xoo ... oox ...&#x ♦ 2 1 2 | 1 2  4 2  1 | 1 2  2  4  1 0 0 |  1 0 0 2  2 0 0 0 | * * * 12 * * * | 0 1 1 0
... ooo3oox ...&#x ♦ 1 1 3 | 0 1  3 3  3 | 0 0  3  3  3 1 0 |  0 1 0 0  3 1 0 0 | * * *  * 8 * * | 0 1 0 1
... ... oox3ooo&#x ♦ 1 1 3 | 0 1  3 3  3 | 0 0  3  3  3 0 1 |  0 0 1 0  3 0 1 0 | * * *  * * 8 * | 0 0 1 1
... .oo3.ox3.oo&#x ♦ 0 1 6 | 0 0  0 6 12 | 0 0  0  0 12 4 4 |  0 0 0 0  0 4 4 1 | * * *  * * * 1 | 0 0 0 2
-------------------+-------+-------------+------------------+-------------------+----------------+--------
x.o o.o3o.x3o.o&#x ♦ 2 0 6 | 1 0 12 0 12 | 0 6 24  0  0 4 4 | 12 8 8 0  0 0 0 1 | 4 4 2  0 0 0 0 | 1 * * *
xoo ooo3oox ...&#x ♦ 2 1 3 | 1 2  6 3  3 | 1 3  6  6  3 1 0 |  3 2 0 3  6 1 0 0 | 1 0 0  3 2 0 0 | * 4 * *
xoo ... oox3ooo&#x ♦ 2 1 3 | 1 2  6 3  3 | 1 3  6  6  3 0 1 |  3 0 2 3  6 0 1 0 | 0 1 0  3 0 2 0 | * * 4 *
... ooo3oox3ooo&#x ♦ 1 1 6 | 0 1  6 6 12 | 0 0 12  6 12 4 4 |  0 4 4 0 12 4 4 1 | 0 0 1  0 4 4 1 | * * * 2