Acronym dotpy
Name dodecateron pyramid,
vertex pyramid of mo
Circumradius 1
Lace city
in approx. ASCII-art
      o      	-- o3o3o3o3o (point)
             
o   A   V   o	-- o3o3x3o3o (dot)

where:
o =  o3o   o3o      (point)
A =  x3o   x3o      (triddip)
V =  o3x   o3x      (bi-inv. triddip)
Confer
uniform relative:
mo  
related CRFs:
dotet  
general polytopal classes:
segmentopeta   fundamental lace prisms  

Incidence matrix according to Dynkin symbol

oo3oo3ox3oo3oo&#x   → height = 1/2
(pt || dot)

o.3o.3o.3o.3o.    | 1  *  20  0 | 90  0  0 | 60 60  0  0  0 | 15 30 15 0 0 | 6 6 0
.o3.o3.o3.o3.o    | * 20   1  9 |  9  9  9 |  9  9  3  9  3 |  3  9  3 3 3 | 3 3 1
------------------+------+-------+----------+----------------+--------------+------
oo3oo3oo3oo3oo&#x | 1  1 | 20  *   9  0  0 |  9  9  0  0  0 |  3  9  3 0 0 | 3 3 0
.. .. .x .. ..    | 0  2 |  * 90 |  1  2  2 |  2  2  1  4  1 |  1  4  1 2 2 | 2 2 1
------------------+------+-------+----------+----------------+--------------+------
.. .. ox .. ..&#x | 1  2 |  2  1 | 90  *  * |  2  2  0  0  0 |  1  4  1 0 0 | 2 2 0
.. .o3.x .. ..    | 0  3 |  0  3 |  * 60  * |  1  0  1  2  0 |  1  2  0 2 1 | 2 1 1
.. .. .x3.o ..    | 0  3 |  0  3 |  *  * 60 |  0  1  0  2  1 |  0  2  1 1 2 | 1 2 1
------------------+------+-------+----------+----------------+--------------+------
.. oo3ox .. ..&#x  1  3 |  3  3 |  3  1  0 | 60  *  *  *  * |  1  2  0 0 0 | 2 1 0
.. .. ox3oo ..&#x  1  3 |  3  3 |  3  0  1 |  * 60  *  *  * |  0  2  1 0 0 | 1 2 0
.o3.o3.x .. ..     0  4 |  0  6 |  0  4  0 |  *  * 15  *  * |  1  0  0 2 0 | 2 0 1
.. .o3.x3.o ..     0  6 |  0 12 |  0  4  4 |  *  *  * 30  * |  0  1  0 1 1 | 1 1 1
.. .. .x3.o3.o     0  4 |  0  6 |  0  0  4 |  *  *  *  * 15 |  0  0  1 0 2 | 0 2 1
------------------+------+-------+----------+----------------+--------------+------
oo3oo3ox .. ..&#x  1  4 |  4  6 |  6  4  0 |  4  0  1  0  0 | 15  *  * * * | 2 0 0
.. oo3ox3oo ..&#x  1  6 |  6 12 | 12  4  4 |  4  4  0  1  0 |  * 30  * * * | 1 1 0
.. .. ox3oo3oo&#x  1  4 |  4  6 |  6  0  4 |  0  4  0  0  1 |  *  * 15 * * | 0 2 0
.o3.o3.x3.o ..     0 10 |  0 30 |  0 20 10 |  0  0  5  5  0 |  *  *  * 6 * | 1 0 1
.. .o3.x3.o3.o     0 10 |  0 30 |  0 10 20 |  0  0  0  5  5 |  *  *  * * 6 | 0 1 1
------------------+------+-------+----------+----------------+--------------+------
oo3oo3ox3oo ..&#x  1 10 | 10 30 | 30 20 10 | 20 10  5  5  0 |  5  5  0 1 0 | 6 * *
.. oo3ox3oo3oo&#x  1 10 | 10 30 | 30 10 20 | 10 20  0  5  5 |  0  5  5 0 1 | * 6 *
.o3.o3.x3.o3.o     0 20 |  0 90 |  0 60 60 |  0  0 15 30 15 |  0  0  0 6 6 | * * 1
or
o.3o.3o.3o.3o.      | 1  *  20  0 | 90   0 | 120  0  0 | 30 30  0 | 12 0
.o3.o3.o3.o3.o      | * 20   1  9 |  9  18 |  18  6  9 |  6  9  6 |  6 1
--------------------+------+-------+--------+-----------+----------+-----
oo3oo3oo3oo3oo&#x   | 1  1 | 20  *   9   0 |  18  0  0 |  6  9  0 |  6 0
.. .. .x .. ..      | 0  2 |  * 90 |  1   4 |   4  2  4 |  2  4  4 |  4 1
--------------------+------+-------+--------+-----------+----------+-----
.. .. ox .. ..&#x   | 1  2 |  2  1 | 90   * |   4  0  0 |  2  4  0 |  4 0
.. .o3.x .. ..    & | 0  3 |  0  3 |  * 120 |   1  1  2 |  1  2  3 |  3 1
--------------------+------+-------+--------+-----------+----------+-----
.. oo3ox .. ..&#x &  1  3 |  3  3 |  3   1 | 120  *  * |  1  2  0 |  3 0
.o3.o3.x .. ..    &  0  4 |  0  6 |  0   4 |   * 30  * |  1  0  2 |  2 1
.. .o3.x3.o ..       0  6 |  0 12 |  0   8 |   *  * 30 |  0  1  2 |  2 1
--------------------+------+-------+--------+-----------+----------+-----
oo3oo3ox .. ..&#x &  1  4 |  4  6 |  6   4 |   4  1  0 | 30  *  * |  2 0
.. oo3ox3oo ..&#x    1  6 |  6 12 | 12   8 |   8  0  1 |  * 30  * |  2 0
.o3.o3.x3.o ..    &  0 10 |  0 30 |  0  30 |   0  5  5 |  *  * 12 |  1 1
--------------------+------+-------+--------+-----------+----------+-----
oo3oo3ox3oo ..&#x &  1 10 | 10 30 | 30  30 |  30  5  5 |  5  5  1 | 12 *
.o3.o3.x3.o3.o       0 20 |  0 90 |  0 120 |   0 30 30 |  0  0 12 |  * 1

ooo3xoo3oox3ooo&#x   → height(1,2) = height(2,3) = sqrt(2/5) = 0.632456
                       height(1,3) = sqrt(3/5) = 0.774597

o..3o..3o..3o..    | 10 *  *   6  1  3  0  0 |  3  6  6  6  3  3  0  0  0 | 3 2  3  6  3  6  1  6  3  0  0 0 0 | 1 3 2 3 2  3  6  1 0 0 0 | 1 1 3 2 0
.o.3.o.3.o.3.o.    |  * 1  *   0 10  0 10  0 |  0  0 30  0  0 30 30  0  0 | 0 0 10 20  0  0  0 30 30 20 10 0 0 | 0 5 5 0 0 10 20 10 5 5 0 | 1 0 5 5 1
..o3..o3..o3..o    |  * * 10   0  0  3  1  6 |  0  0  0  3  6  3  6  6  3 | 0 0  0  0  1  6  3  3  6  6  3 2 3 | 0 0 0 2 3  1  6  3 2 3 1 | 0 1 2 3 1
-------------------+---------+----------------+----------------------------+------------------------------------+--------------------------+----------
... x.. ... ...    |  2 0  0 | 30  *  *  *  * |  1  2  1  1  0  0  0  0  0 | 2 1  1  2  1  2  0  1  0  0  0 0 0 | 1 2 1 2 1  1  2  0 0 0 0 | 1 1 2 1 0
oo.3oo.3oo.3oo.&#x |  1 1  0 |  * 10  *  *  *   0  0  6  0  0  3  0  0  0 | 0 0  3  6  0  0  0  6  3  0  0 0 0 | 0 3 2 0 0  3  6  1 0 0 0 | 1 0 3 2 0
o.o3o.o3o.o3o.o&#x |  1 0  1 |  *  * 30  *  * |  0  0  0  2  2  1  0  0  0 | 0 0  0  0  1  4  1  2  2  0  0 0 0 | 0 0 0 2 2  1  4  1 0 0 0 | 0 1 2 2 0
.oo3.oo3.oo3.oo&#x |  0 1  1 |  *  *  * 10  *   0  0  0  0  0  3  6  0  0 | 0 0  0  0  0  0  0  3  6  6  3 0 0 | 0 0 0 0 0  1  6  3 2 3 0 | 0 0 2 3 1
... ... ..x ...    |  0 0  2 |  *  *  *  * 30 |  0  0  0  0  1  0  1  2  1 | 0 0  0  0  0  2  1  0  1  2  1 1 2 | 0 0 0 1 2  0  2  1 1 2 1 | 0 1 1 2 1
-------------------+---------+----------------+----------------------------+------------------------------------+--------------------------+----------
o..3x.. ... ...    |  3 0  0 |  3  0  0  0  0 | 10  *  *  *  *  *  *  *  * | 2 0  1  0  1  0  0  0  0  0  0 0 0 | 1 2 0 2 0  1  0  0 0 0 0 | 1 1 2 0 0
... x..3o.. ...    |  3 0  0 |  3  0  0  0  0 |  * 20  *  *  *  *  *  *  * | 1 1  0  1  0  1  0  0  0  0  0 0 0 | 1 1 1 1 1  0  1  0 0 0 0 | 1 1 1 1 0
... xo. ... ...&#x |  2 1  0 |  1  2  0  0  0 |  *  * 30  *  *  *  *  *  * | 0 0  1  2  0  0  0  1  0  0  0 0 0 | 0 2 1 0 0  1  2  0 0 0 0 | 1 0 2 1 0
... x.o ... ...&#x |  2 0  1 |  1  0  2  0  0 |  *  *  * 30  *  *  *  *  * | 0 0  0  0  1  2  0  1  0  0  0 0 0 | 0 0 0 2 1  1  2  0 0 0 0 | 0 1 2 1 0
... ... o.x ...&#x |  1 0  2 |  0  0  2  0  1 |  *  *  *  * 30  *  *  *  * | 0 0  0  0  0  2  1  0  1  0  0 0 0 | 0 0 0 1 2  0  2  1 0 0 0 | 0 1 1 2 0
ooo3ooo3ooo3ooo&#x |  1 1  1 |  0  1  1  1  0 |  *  *  *  *  * 30  *  *  * | 0 0  0  0  0  0  0  2  2  0  0 0 0 | 0 0 0 0 0  1  4  1 0 0 0 | 0 0 2 2 0
... ... .ox ...&#x |  0 1  2 |  0  0  0  2  1 |  *  *  *  *  *  * 30  *  * | 0 0  0  0  0  0  0  0  1  2  1 0 0 | 0 0 0 0 0  0  2  1 1 2 0 | 0 0 1 2 1
... ..o3..x ...    |  0 0  3 |  0  0  0  0  3 |  *  *  *  *  *  *  * 20  * | 0 0  0  0  0  1  0  0  0  1  0 1 1 | 0 0 0 1 1  0  1  0 1 1 1 | 0 1 1 1 1
... ... ..x3..o    |  0 0  3 |  0  0  0  0  3 |  *  *  *  *  *  *  *  * 10 | 0 0  0  0  0  0  1  0  0  0  1 0 2 | 0 0 0 0 2  0  0  1 0 2 1 | 0 1 0 2 1
-------------------+---------+----------------+----------------------------+------------------------------------+--------------------------+----------
o..3x..3o.. ...      6 0  0 | 12  0  0  0  0 |  4  4  0  0  0  0  0  0  0 | 5 *  *  *  *  *  *  *  *  *  * * * | 1 1 0 1 0  0  0  0 0 0 0 | 1 1 1 0 0
... x..3o..3o..      4 0  0 |  6  0  0  0  0 |  0  4  0  0  0  0  0  0  0 | * 5  *  *  *  *  *  *  *  *  * * * | 1 0 1 0 1  0  0  0 0 0 0 | 1 1 0 1 0
oo.3xo. ... ...&#x   3 1  0 |  3  3  0  0  0 |  1  0  3  0  0  0  0  0  0 | * * 10  *  *  *  *  *  *  *  * * * | 0 2 0 0 0  1  0  0 0 0 0 | 1 0 2 0 0
... xo.3oo. ...&#x   3 1  0 |  3  3  0  0  0 |  0  1  3  0  0  0  0  0  0 | * *  * 20  *  *  *  *  *  *  * * * | 0 1 1 0 0  0  1  0 0 0 0 | 1 0 1 1 0
o.o3x.o ... ...&#x   3 0  1 |  3  0  3  0  0 |  1  0  0  3  0  0  0  0  0 | * *  *  * 10  *  *  *  *  *  * * * | 0 0 0 2 0  1  0  0 0 0 0 | 0 1 2 0 0
... x.o3o.x ...&#x   3 0  3 |  3  0  6  0  3 |  0  1  0  3  3  0  0  1  0 | * *  *  *  * 20  *  *  *  *  * * * | 0 0 0 1 1  0  1  0 0 0 0 | 0 1 1 1 0
... ... o.x3o.o&#x   1 0  3 |  0  0  3  0  3 |  0  0  0  0  3  0  0  0  1 | * *  *  *  *  * 10  *  *  *  * * * | 0 0 0 0 2  0  0  1 0 0 0 | 0 1 0 2 0
... xoo ... ...&#x   2 1  1 |  1  2  2  1  0 |  0  0  1  1  0  2  0  0  0 | * *  *  *  *  *  * 30  *  *  * * * | 0 0 0 0 0  1  2  0 0 0 0 | 0 0 2 1 0
... ... oox ...&#x   1 1  2 |  0  1  2  2  1 |  0  0  0  0  1  2  1  0  0 | * *  *  *  *  *  *  * 30  *  * * * | 0 0 0 0 0  0  2  1 0 0 0 | 0 0 1 2 0
... .oo3.ox ...&#x   0 1  3 |  0  0  0  3  3 |  0  0  0  0  0  0  3  1  0 | * *  *  *  *  *  *  *  * 20  * * * | 0 0 0 0 0  0  1  0 1 1 0 | 0 0 1 1 1
... ... .ox3.oo&#x   0 1  3 |  0  0  0  3  3 |  0  0  0  0  0  0  3  0  1 | * *  *  *  *  *  *  *  *  * 10 * * | 0 0 0 0 0  0  0  1 0 2 0 | 0 0 0 2 1
..o3..o3..x ...      0 0  4 |  0  0  0  0  6 |  0  0  0  0  0  0  0  4  0 | * *  *  *  *  *  *  *  *  *  * 5 * | 0 0 0 1 0  0  0  0 1 0 1 | 0 1 1 0 1
... ..o3..x3..o      0 0  6 |  0  0  0  0 12 |  0  0  0  0  0  0  0  4  4 | * *  *  *  *  *  *  *  *  *  * * 5 | 0 0 0 0 1  0  0  0 0 1 1 | 0 1 0 1 1
-------------------+---------+----------------+----------------------------+------------------------------------+--------------------------+----------
o..3x..3o..3o..     10 0  0 | 30  0  0  0  0 | 10 20  0  0  0  0  0  0  0 | 5 5  0  0  0  0  0  0  0  0  0 0 0 | 1 * * * *  *  *  * * * * | 1 1 0 0 0
oo.3xo.3oo. ...&#x   6 1  0 | 12  6  0  0  0 |  4  4 12  0  0  0  0  0  0 | 1 0  4  4  0  0  0  0  0  0  0 0 0 | * 5 * * *  *  *  * * * * | 1 0 1 0 0
... xo.3oo.3oo.&#x   4 1  0 |  6  4  0  0  0 |  0  4  6  0  0  0  0  0  0 | 0 1  0  4  0  0  0  0  0  0  0 0 0 | * * 5 * *  *  *  * * * * | 1 0 0 1 0
o.o3x.o3o.x ...&#x   6 0  4 | 12  0 12  0  6 |  4  4  0 12  6  0  0  4  0 | 1 0  0  0  4  4  0  0  0  0  0 1 0 | * * * 5 *  *  *  * * * * | 0 1 1 0 0
... x.o3o.x3o.o&#x   4 0  6 |  6  0 12  0 12 |  0  4  0  6 12  0  0  4  4 | 0 1  0  0  0  4  4  0  0  0  0 0 1 | * * * * 5  *  *  * * * * | 0 1 0 1 0
ooo3xoo ... ...&#x   3 1  1 |  3  3  3  1  0 |  1  0  3  3  0  3  0  0  0 | 0 0  1  0  1  0  0  3  0  0  0 0 0 | * * * * * 10  *  * * * * | 0 0 2 0 0
... xoo3oox ...&#x   3 1  3 |  3  3  6  3  3 |  0  1  3  3  3  6  3  1  0 | 0 0  0  1  0  1  0  3  3  1  0 0 0 | * * * * *  * 20  * * * * | 0 0 1 1 0
... ... oox3ooo&#x   1 1  3 |  0  1  3  3  3 |  0  0  0  0  3  3  3  0  1 | 0 0  0  0  0  0  1  0  3  0  1 0 0 | * * * * *  *  * 10 * * * | 0 0 0 2 0
.oo3.oo3.ox ...&#x   0 1  4 |  0  0  0  4  6 |  0  0  0  0  0  0  6  4  0 | 0 0  0  0  0  0  0  0  0  4  0 1 0 | * * * * *  *  *  * 5 * * | 0 0 1 0 1
... .oo3.ox3.oo&#x   0 1  6 |  0  0  0  6 12 |  0  0  0  0  0  0 12  4  4 | 0 0  0  0  0  0  0  0  0  4  4 0 1 | * * * * *  *  *  * * 5 * | 0 0 0 1 1
..o3..o3..x3..o      0 0 10 |  0  0  0  0 30 |  0  0  0  0  0  0  0 20 10 | 0 0  0  0  0  0  0  0  0  0  0 5 5 | * * * * *  *  *  * * * 1 | 0 1 0 0 1
-------------------+---------+----------------+----------------------------+------------------------------------+--------------------------+----------
oo.3xo.3oo.3oo.&#x  10 1  0 | 30 10  0  0  0 | 10 20 30  0  0  0  0  0  0 | 5 5 10 20  0  0  0  0  0  0  0 0 0 | 1 5 5 0 0  0  0  0 0 0 0 | 1 * * * *
o.o3x.o3o.x3o.o&#x  10 0 10 | 30  0 30  0 30 | 10 20  0 30 30  0  0 20 10 | 5 5  0  0 10 20 10  0  0  0  0 5 5 | 1 0 0 5 5  0  0  0 0 0 1 | * 1 * * *
ooo3xoo3oox ...&#x   6 1  4 | 12  6 12  4  6 |  4  4 12 12  6 12  6  4  0 | 1 0  4  4  4  4  0 12  6  4  0 1 0 | 0 1 0 1 0  4  4  0 1 0 0 | * * 5 * *
... xoo3oox3ooo&#x   4 1  6 |  6  4 12  6 12 |  0  4  6  6 12 12 12  4  4 | 0 1  0  4  0  4  4  6 12  4  4 0 1 | 0 0 1 0 1  0  4  4 0 1 0 | * * * 5 *
.oo3.oo3.ox3.oo&#x   0 1 10 |  0  0  0 10 30 |  0  0  0  0  0  0 30 20 10 | 0 0  0  0  0  0  0  0  0 20 10 5 5 | 0 0 0 0 0  0  0  0 5 5 1 | * * * * 1

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