Acronym octpyp, line||ope
Name octahedron-prismatic wedge,
line atop ope,
octahedral-pyramid prism,
half of hexip
Circumradius sqrt(3)/2 = 0.866025
Lace city
in approx. ASCII-art
    o3o x    
             
             
x3o x   o3x x
o3o4o   o3o4o
             
             
x3o4o   x3o4o
Confer
uniform relative:
hexip  
general polytopal classes:
segmentotera   lace simplices  

Incidence matrix according to Dynkin symbol

xx ox3oo4oo&#x   → height = 1/sqrt(2) = 0.707107
(line || ope)

o. o.3o.4o.    | 2  * | 1  6 0  0 | 6 12  0  0 | 12  8 0 0 | 8 1 0
.o .o3.o4.o    | * 12 | 0  1 1  4 | 1  4  4  4 |  4  4 4 1 | 4 1 1
---------------+------+-----------+------------+-----------+------
x. .. .. ..    | 2  0 | 1  * *  *  6  0  0  0 | 12  0 0 0 | 8 0 0
oo oo3oo4oo&#x | 1  1 | * 12 *  * | 1  4  0  0 |  4  4 0 0 | 4 1 0
.x .. .. ..    | 0  2 | *  * 6  *  1  0  4  0 |  4  0 4 0 | 4 0 1
.. .x .. ..    | 0  2 | *  * * 24 | 0  1  1  2 |  1  2 2 1 | 2 1 1
---------------+------+-----------+------------+-----------+------
xx .. .. ..&#x | 2  2 | 1  2 1  0 | 6  *  *  * |  4  0 0 0 | 4 0 0
.. ox .. ..&#x | 1  2 | 0  2 0  1 | * 24  *  * |  1  2 0 0 | 2 1 0
.x .x .. ..    | 0  4 | 0  0 2  2 | *  * 12  * |  1  0 2 0 | 2 0 1
.. .x3.o ..    | 0  3 | 0  0 0  3 | *  *  * 16 |  0  1 1 1 | 1 1 1
---------------+------+-----------+------------+-----------+------
xx ox .. ..&#x  2  4 | 1  4 2  2 | 2  2  1  0 | 12  * * * | 2 0 0
.. ox3oo ..&#x  1  3 | 0  3 0  3 | 0  3  0  1 |  * 16 * * | 1 1 0
.x .x3.o ..     0  6 | 0  0 3  6 | 0  0  3  2 |  *  * 8 * | 1 0 1
.. .x3.o4.o     0  6 | 0  0 0 12 | 0  0  0  8 |  *  * * 2 | 0 1 1
---------------+------+-----------+------------+-----------+------
xx ox3oo ..&#x  2  6 | 1  6 3  6 | 3  6  3  2 |  3  2 1 0 | 8 * *
.. ox3oo4oo&#x  1  6 | 0  6 0 12 | 0 12  0  8 |  0  8 0 1 | * 2 *
.x .x3.o4.o     0 12 | 0  0 6 24 | 0  0 12 16 |  0  0 8 2 | * * 1

xx oo3ox3oo&#x   → height = 1/sqrt(2) = 0.707107
(line || ope)

o. o.3o.3o.    | 2  * | 1  6 0  0 | 6 12  0 0 0 | 12 4 4 0 0 0 | 4 4 1 0
.o .o3.o3.o    | * 12 | 0  1 1  4 | 1  4  4 2 2 |  4 2 2 2 2 1 | 2 2 1 1
---------------+------+-----------+-------------+--------------+--------
x. .. .. ..    | 2  0 | 1  * *  *  6  0  0 0 0 | 12 0 0 0 0 0 | 4 4 0 0
oo oo3oo3oo&#x | 1  1 | * 12 *  * | 1  4  0 0 0 |  4 2 2 0 0 0 | 2 2 1 0
.x .. .. ..    | 0  2 | *  * 6  *  1  0  4 0 0 |  4 0 0 2 2 0 | 2 2 0 1
.. .. .x ..    | 0  2 | *  * * 24 | 0  1  1 1 1 |  1 1 1 1 1 1 | 1 1 1 1
---------------+------+-----------+-------------+--------------+--------
xx .. .. ..&#x | 2  2 | 1  2 1  0 | 6  *  * * * |  4 0 0 0 0 0 | 2 2 0 0
.. .. ox ..&#x | 1  2 | 0  2 0  1 | * 24  * * * |  1 1 1 0 0 0 | 1 1 1 0
.x .. .x ..    | 0  4 | 0  0 2  2 | *  * 12 * * |  1 0 0 1 1 0 | 1 1 0 1
.. .o3.x ..    | 0  3 | 0  0 0  3 | *  *  * 8 * |  0 1 0 1 0 1 | 1 0 1 1
.. .. .x3.o    | 0  3 | 0  0 0  3 | *  *  * * 8 |  0 0 1 0 1 1 | 0 1 1 1
---------------+------+-----------+-------------+--------------+--------
xx .. ox ..&#x  2  4 | 1  4 2  2 | 2  2  1 0 0 | 12 * * * * * | 1 1 0 0
.. oo3ox ..&#x  1  3 | 0  3 0  3 | 0  3  0 1 0 |  * 8 * * * * | 1 0 1 0
.. .. ox3oo&#x  1  3 | 0  3 0  3 | 0  3  0 0 1 |  * * 8 * * * | 0 1 1 0
.x .o3.x ..     0  6 | 0  0 3  6 | 0  0  3 2 0 |  * * * 4 * * | 1 0 0 1
.x .. .x3.o     0  6 | 0  0 3  6 | 0  0  3 0 2 |  * * * * 4 * | 0 1 0 1
.. .o3.x3.o     0  6 | 0  0 0 12 | 0  0  0 4 4 |  * * * * * 2 | 0 0 1 1
---------------+------+-----------+-------------+--------------+--------
xx oo3ox ..&#x  2  6 | 1  6 3  6 | 3  6  3 2 0 |  3 2 0 1 0 0 | 4 * * *
xx .. ox3oo&#x  2  6 | 1  6 3  6 | 3  6  3 0 2 |  3 0 2 0 1 0 | * 4 * *
.. oo3ox3oo&#x  1  6 | 0  6 0 12 | 0 12  0 4 4 |  0 4 4 0 0 1 | * * 2 *
.x .o3.x3.o     0 12 | 0  0 6 24 | 0  0 12 8 8 |  0 0 0 4 4 2 | * * * 1

xxx oox3oxo&#x   → height(1,2) = height(1,3) = height(2,3) = sqrt(2/3) = 0.816497

o.. o..3o..    | 2 * * | 1 3 3 0 0  0 0 0 | 3 3  6 3 3 0 0 0 0 0 0 0 | 3 1 6 3 3 3 1 0 0 0 0 0 | 1 3 3 1 1 0
.o. .o.3.o.    | * 6 * | 0 1 0 1 2  2 0 0 | 1 2  2 0 0 2 1 2 1 2 0 0 | 2 1 2 1 2 0 0 1 1 2 1 0 | 1 1 2 1 0 1
..o ..o3..o    | * * 6 | 0 0 1 0 0  2 1 2 | 0 0  2 1 2 0 0 2 2 1 2 1 | 0 0 2 2 1 2 1 0 2 1 1 1 | 0 2 1 1 1 1
---------------+-------+------------------+--------------------------+-------------------------+------------
x.. ... ...    | 2 0 0 | 1 * * * *  * * *  3 0  0 3 0 0 0 0 0 0 0 0 | 3 0 6 0 0 3 0 0 0 0 0 0 | 1 3 3 0 1 0
oo. oo.3oo.&#x | 1 1 0 | * 6 * * *  * * * | 1 2  2 0 0 0 0 0 0 0 0 0 | 2 1 2 1 2 0 0 0 0 0 0 0 | 1 1 2 1 0 0
o.o o.o3o.o&#x | 1 0 1 | * * 6 * *  * * * | 0 0  2 1 2 0 0 0 0 0 0 0 | 0 0 2 2 1 2 1 0 0 0 0 0 | 0 2 1 1 1 0
.x. ... ...    | 0 2 0 | * * * 3 *  * * *  1 0  0 0 0 2 0 2 0 0 0 0 | 2 0 2 0 0 0 0 1 1 2 0 0 | 1 1 2 0 0 1
... ... .x.    | 0 2 0 | * * * * 6  * * * | 0 1  0 0 0 1 1 0 0 1 0 0 | 1 1 0 0 1 0 0 1 0 1 1 0 | 1 0 1 1 0 1
.oo .oo3.oo&#x | 0 1 1 | * * * * * 12 * * | 0 0  1 0 0 0 0 1 1 1 0 0 | 0 0 1 1 1 0 0 0 1 1 1 0 | 0 1 1 1 0 1
..x ... ...    | 0 0 2 | * * * * *  * 3 *  0 0  0 1 0 0 0 2 0 0 2 0 | 0 0 2 0 0 2 0 0 2 1 0 1 | 0 2 1 0 1 1
... ..x ...    | 0 0 2 | * * * * *  * * 6 | 0 0  0 0 1 0 0 0 1 0 1 1 | 0 0 0 1 0 1 1 0 1 0 1 1 | 0 1 0 1 1 1
---------------+-------+------------------+--------------------------+-------------------------+------------
xx. ... ...&#x | 2 2 0 | 1 2 0 1 0  0 0 0 | 3 *  * * * * * * * * * * | 2 0 2 0 0 0 0 0 0 0 0 0 | 1 1 2 0 0 0
... ... ox.&#x | 1 2 0 | 0 2 0 0 1  0 0 0 | * 6  * * * * * * * * * * | 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 1 1 0 0  1 0 0 | * * 12 * * * * * * * * * | 0 0 1 1 1 0 0 0 0 0 0 0 | 0 1 1 1 0 0
x.x ... ...&#x | 2 0 2 | 1 0 2 0 0  0 1 0 | * *  * 3 * * * * * * * * | 0 0 2 0 0 2 0 0 0 0 0 0 | 0 2 1 0 1 0
... o.x ...&#x | 1 0 2 | 0 0 2 0 0  0 0 1 | * *  * * 6 * * * * * * * | 0 0 0 1 0 1 1 0 0 0 0 0 | 0 1 0 1 1 0
.x. ... .x.    | 0 4 0 | 0 0 0 2 2  0 0 0 | * *  * * * 3 * * * * * * | 1 0 0 0 0 0 0 1 0 1 0 0 | 1 0 1 0 0 1
... .o.3.x.    | 0 3 0 | 0 0 0 0 3  0 0 0 | * *  * * * * 2 * * * * * | 0 1 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  2 1 0 | * *  * * * * * 6 * * * * | 0 0 1 0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
... .ox ...&#x | 0 1 2 | 0 0 0 0 0  2 0 1 | * *  * * * * * * 6 * * * | 0 0 0 1 0 0 0 0 1 0 1 0 | 0 1 0 1 0 1
... ... .xo&#x | 0 2 1 | 0 0 0 0 1  2 0 0 | * *  * * * * * * * 6 * * | 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 2 2 | * *  * * * * * * * * 3 * | 0 0 0 0 0 1 0 0 1 0 0 1 | 0 1 0 0 1 1
... ..x3..o    | 0 0 3 | 0 0 0 0 0  0 0 3 | * *  * * * * * * * * * 2 | 0 0 0 0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
---------------+-------+------------------+--------------------------+-------------------------+------------
xx. ... ox.&#x  2 4 0 | 1 4 0 2 2  0 0 0 | 2 2  0 0 0 1 0 0 0 0 0 0 | 3 * * * * * * * * * * * | 1 0 1 0 0 0
... oo.3ox.&#x  1 3 0 | 0 3 0 0 3  0 0 0 | 0 3  0 0 0 0 1 0 0 0 0 0 | * 2 * * * * * * * * * * | 1 0 0 1 0 0
xxx ... ...&#x  2 2 2 | 1 2 2 1 0  2 1 0 | 1 0  2 1 0 0 0 1 0 0 0 0 | * * 6 * * * * * * * * * | 0 1 1 0 0 0
... oox ...&#x  1 1 2 | 0 1 2 0 0  2 0 1 | 0 0  2 0 1 0 0 0 1 0 0 0 | * * * 6 * * * * * * * * | 0 1 0 1 0 0
... ... oxo&#x  1 2 1 | 0 2 1 0 1  2 0 0 | 0 1  2 0 0 0 0 0 0 1 0 0 | * * * * 6 * * * * * * * | 0 0 1 1 0 0
x.x o.x ...&#x  2 0 4 | 1 0 4 0 0  0 2 2 | 0 0  0 2 2 0 0 0 0 0 1 0 | * * * * * 3 * * * * * * | 0 1 0 0 1 0
... o.x3o.o&#x  1 0 3 | 0 0 3 0 0  0 0 3 | 0 0  0 0 3 0 0 0 0 0 0 1 | * * * * * * 2 * * * * * | 0 0 0 1 1 0
.x. .o.3.x.     0 6 0 | 0 0 0 3 6  0 0 0 | 0 0  0 0 0 3 2 0 0 0 0 0 | * * * * * * * 1 * * * * | 1 0 0 0 0 1
.xx .ox ...&#x  0 2 4 | 0 0 0 1 0  4 2 2 | 0 0  0 0 0 0 0 2 2 0 1 0 | * * * * * * * * 3 * * * | 0 1 0 0 0 1
.xx ... .xo&#x  0 4 2 | 0 0 0 2 2  4 1 0 | 0 0  0 0 0 1 0 2 0 2 0 0 | * * * * * * * * * 3 * * | 0 0 1 0 0 1
... .ox3.xo&#x  0 3 3 | 0 0 0 0 3  6 0 3 | 0 0  0 0 0 0 1 0 3 3 0 1 | * * * * * * * * * * 2 * | 0 0 0 1 0 1
..x ..x3..o     0 0 6 | 0 0 0 0 0  0 3 6 | 0 0  0 0 0 0 0 0 0 0 3 2 | * * * * * * * * * * * 1 | 0 0 0 0 1 1
---------------+-------+------------------+--------------------------+-------------------------+------------
xx. oo.3ox.&#x  2 6 0 | 1 6 0 3 6  0 0 0 | 3 6  0 0 0 3 2 0 0 0 0 0 | 3 2 0 0 0 0 0 1 0 0 0 0 | 1 * * * * *
xxx oox ...&#x  2 2 4 | 1 2 4 1 0  4 2 2 | 1 0  4 2 2 0 0 2 2 0 1 0 | 0 0 2 2 0 1 0 0 1 0 0 0 | * 3 * * * *
xxx ... oxo&#x  2 4 2 | 1 4 2 2 2  4 1 0 | 2 2  4 1 0 1 0 2 0 2 0 0 | 1 0 2 0 2 0 0 0 0 1 0 0 | * * 3 * * *
... oox3oxo&#x  1 3 3 | 0 3 3 0 3  6 0 3 | 0 3  6 0 3 0 1 0 3 3 0 1 | 0 1 0 3 3 0 1 0 0 0 1 0 | * * * 2 * *
x.x o.x3o.o&#x  2 0 6 | 1 0 6 0 0  0 3 6 | 0 0  0 3 6 0 0 0 0 0 3 2 | 0 0 0 0 0 3 2 0 0 0 0 1 | * * * * 1 *
.xx .ox3.xo&#x  0 6 6 | 0 0 0 3 6 12 3 6 | 0 0  0 0 0 3 2 6 6 6 3 2 | 0 0 0 0 0 0 0 1 3 3 2 1 | * * * * * 1

ooxx3oooo4oooo&#xr   → height(1,2) = height(3,4) = 1
                       height(2,3) = height(1,4) = 1/sqrt(2) = 0.707107

o...3o...4o...     | 1 * * * | 1 6 0  0 0  0 | 6 12  0 0  0 0 | 12 8 0 0 0 0 | 8 1 0 0
.o..3.o..4.o..     | * 1 * * | 1 0 6  0 0  0 | 6  0 12 0  0 0 | 12 0 8 0 0 0 | 8 0 1 0
..o.3..o.4..o.     | * * 6 * | 0 0 1  4 1  0 | 1  0  4 4  4 0 |  4 0 4 1 4 0 | 4 0 1 1
...o3...o4...o     | * * * 6 | 0 1 0  0 1  4 | 1  4  0 0  4 4 |  4 4 0 0 4 1 | 4 1 0 1
-------------------+---------+---------------+----------------+--------------+--------
oo..3oo..4oo..&#x  | 1 1 0 0 | 1 * *  * *  * | 6  0  0 0  0 0 | 12 0 0 0 0 0 | 8 0 0 0
o..o3o..o4o..o&#x  | 1 0 0 1 | * 6 *  * *  * | 1  4  0 0  0 0 |  4 4 0 0 0 0 | 4 1 0 0
.oo.3.oo.4.oo.&#x  | 0 1 1 0 | * * 6  * *  * | 1  0  4 0  0 0 |  4 0 4 0 0 0 | 4 0 1 0
..x. .... ....     | 0 0 2 0 | * * * 12 *  * | 0  0  1 2  1 0 |  1 0 2 1 2 0 | 2 0 1 1
..oo3..oo4..oo&#x  | 0 0 1 1 | * * *  * 6  * | 1  0  0 0  4 0 |  4 0 0 0 4 0 | 4 0 0 1
...x .... ....     | 0 0 0 2 | * * *  * * 12 | 0  1  0 0  1 2 |  1 2 0 0 2 1 | 2 1 0 1
-------------------+---------+---------------+----------------+--------------+--------
oooo3oooo4oooo&#xr | 1 1 1 1 | 1 1 1  0 1  0 | 6  *  * *  * * |  4 0 0 0 0 0 | 4 0 0 0
o..x .... ....&#x  | 1 0 0 2 | 0 2 0  0 0  1 | * 12  * *  * * |  1 2 0 0 0 0 | 2 1 0 0
.ox. .... ....&#x  | 0 1 2 0 | 0 0 2  1 0  0 | *  * 12 *  * * |  1 0 2 0 0 0 | 2 0 1 0
..x.3..o. ....     | 0 0 3 0 | 0 0 0  3 0  0 | *  *  * 8  * * |  0 0 1 1 1 0 | 1 0 1 1
..xx .... ....&#x  | 0 0 2 2 | 0 0 0  1 2  1 | *  *  * * 12 * |  1 0 0 0 2 0 | 2 0 0 1
...x3...o ....     | 0 0 0 3 | 0 0 0  0 0  3 | *  *  * *  * 8 |  0 1 0 0 1 1 | 1 1 0 1
-------------------+---------+---------------+----------------+--------------+--------
ooxx .... ....&#xr  1 1 2 2 | 1 2 2  1 2  1 | 2  1  1 0  1 0 | 12 * * * * * | 2 0 0 0
o..x3o..o ....&#x   1 0 0 3 | 0 3 0  0 0  3 | 0  3  0 0  0 1 |  * 8 * * * * | 1 1 0 0
.ox.3.oo. ....&#x   0 1 3 0 | 0 0 3  3 0  0 | 0  0  3 1  0 0 |  * * 8 * * * | 1 0 1 0
..x.3..o.4..o.      0 0 6 0 | 0 0 0 12 0  0 | 0  0  0 8  0 0 |  * * * 1 * * | 0 0 1 1
..xx3..oo ....&#x   0 0 3 3 | 0 0 0  3 3  3 | 0  0  0 1  3 1 |  * * * * 8 * | 1 0 0 1
...x3...o4...o      0 0 0 6 | 0 0 0  0 0 12 | 0  0  0 0  0 8 |  * * * * * 1 | 0 1 0 1
-------------------+---------+---------------+----------------+--------------+--------
ooxx3oooo ....&#xr  1 1 3 3 | 1 3 3  3 3  3 | 3  3  3 1  3 1 |  3 1 1 0 1 0 | 8 * * *
o..x3o..o4o..o&#x   1 0 0 6 | 0 6 0  0 0 12 | 0 12  0 0  0 8 |  0 8 0 0 0 1 | * 1 * *
.ox.3.oo.4.oo.&#x   0 1 6 0 | 0 0 6 12 0  0 | 0  0 12 8  0 0 |  0 0 8 1 0 0 | * * 1 *
..xx3..oo4..oo&#x   0 0 6 6 | 0 0 0 12 6 12 | 0  0  0 8 12 8 |  0 0 0 1 8 1 | * * * 1


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