Acronym opeaco
Name octahedron-prism atop cuboctahedron,
diminished 1/4-lune of rat
Circumradius 1
Lace city
in approx. ASCII-art
       x3o4o
            
            
            
x3o4o  o3x4o
    x o3x   x x3o    
                     
                     
o x3o   o x3x   o o3x
Confer
uniform relative:
rat  
related segmentochora:
octpy || octaco   pexhix   opeah  
general polytopal classes:
segmentotera   lace simplices  

Incidence matrix according to Dynkin symbol

xo xo3ox4oo&#x   → height = 1/2

o. o.3o.4o.    | 12  * | 1  4  4  0 |  4  4  4  4  4 0 0 | 4 1  4  4  4  1 0 | 1 4 1 1
.o .o3.o4.o    |  * 12 | 0  0  4  4 |  0  0  2  2  8 2 2 | 0 0  1  4  4  4 1 | 0 2 2 2
---------------+-------+------------+--------------------+-------------------+--------
x. .. .. ..    |  2  0 | 6  *  *  *   4  0  4  0  0 0 0 | 4 0  4  4  0  0 0 | 1 4 1 0
.. x. .. ..    |  2  0 | * 24  *  * |  1  2  0  1  0 0 0 | 2 1  1  0  2  0 0 | 1 2 0 1
oo oo3oo4oo&#x |  1  1 | *  * 48  * |  0  0  1  1  2 0 0 | 0 0  1  2  2  1 0 | 0 2 1 1
.. .. .x ..    |  0  2 | *  *  * 24 |  0  0  0  0  2 1 1 | 0 0  0  1  2  2 1 | 0 1 1 2
---------------+-------+------------+--------------------+-------------------+--------
x. x. .. ..    |  4  0 | 2  2  0  0 | 12  *  *  *  * * * | 2 0  1  0  0  0 0 | 1 2 0 0
.. x.3o. ..    |  3  0 | 0  3  0  0 |  * 16  *  *  * * * | 1 1  0  0  1  0 0 | 1 1 0 1
xo .. .. ..&#x |  2  1 | 1  0  2  0 |  *  * 24  *  * * * | 0 0  1  2  0  0 0 | 0 2 1 0
.. xo .. ..&#x |  2  1 | 0  1  2  0 |  *  *  * 24  * * * | 0 0  1  0  2  0 0 | 0 2 0 1
.. .. ox ..&#x |  1  2 | 0  0  2  1 |  *  *  *  * 48 * * | 0 0  0  1  1  1 0 | 0 1 1 1
.. .o3.x ..    |  0  3 | 0  0  0  3 |  *  *  *  *  * 8 * | 0 0  0  0  2  0 1 | 0 1 0 2
.. .. .x4.o    |  0  4 | 0  0  0  4 |  *  *  *  *  * * 6 | 0 0  0  0  0  2 1 | 0 0 1 2
---------------+-------+------------+--------------------+-------------------+--------
x. x.3o. ..      6  0 | 3  6  0  0 |  3  2  0  0  0 0 0 | 8 *  *  *  *  * * | 1 1 0 0
.. x.3o.4o.      6  0 | 0 12  0  0 |  0  8  0  0  0 0 0 | * 2  *  *  *  * * | 1 0 0 1
xo xo .. ..&#x   4  1 | 2  2  4  0 |  1  0  2  2  0 0 0 | * * 12  *  *  * * | 0 2 0 0
xo .. ox ..&#x   2  2 | 1  0  4  1 |  0  0  2  0  2 0 0 | * *  * 24  *  * * | 0 1 1 0
.. xo3ox ..&#x   3  3 | 0  3  6  3 |  0  1  0  3  3 1 0 | * *  *  * 16  * * | 0 1 0 1
.. .. ox4oo&#x   1  4 | 0  0  4  4 |  0  0  0  0  4 0 1 | * *  *  *  * 12 * | 0 0 1 1
.. .o3.x4o       0 12 | 0  0  0 24 |  0  0  0  0  0 8 6 | * *  *  *  *  * 1 | 0 0 0 2
---------------+-------+------------+--------------------+-------------------+--------
x. x.3o.4o.     12  0 | 6 24  0  0 | 12 16  0  0  0 0 0 | 8 2  0  0  0  0 0 | 1 * * *
xo xo3ox ..&#x   6  3 | 3  6 12  3 |  3  2  6  6  6 1 0 | 1 0  3  3  2  0 0 | * 8 * *
xo .. ox4oo&#x   2  4 | 1  0  8  4 |  0  0  4  0  8 0 1 | 0 0  0  4  0  2 0 | * * 6 *
.. xo3ox4oo&#x   6 12 | 0 12 24 24 |  0  8  0 12 24 8 6 | 0 1  0  0  8  6 1 | * * * 2

xo ox3xo3ox&#x   → height = 1/2

o. o.3o.3o.    | 12  * | 1  4  4  0  0 |  4 2 2  4  2  4  2 0 0 0 | 2 2 1  2  4  2 2  1 2 0 | 1 2 1 2 1
.o .o3.o3.o    |  * 12 | 0  0  4  2  2 |  0 0 0  2  4  2  4 1 2 1 | 0 0 0  2  1  2 2  4 2 1 | 0 1 2 1 2
---------------+-------+---------------+--------------------------+-------------------------+----------
x. .. .. ..    |  2  0 | 6  *  *  *  *   4 0 0  4  0  0  0 0 0 0 | 2 2 0  2  4  2 0  0 0 0 | 1 2 1 2 0
.. .. x. ..    |  2  0 | * 24  *  *  * |  1 1 1  0  0  1  0 0 0 0 | 1 1 1  0  1  0 1  0 1 0 | 1 1 0 1 1
oo oo3oo3oo&#x |  1  1 | *  * 48  *  * |  0 0 0  1  1  1  1 0 0 0 | 0 0 0  1  1  1 1  1 1 0 | 0 1 1 1 1
.. .x .. ..    |  0  2 | *  *  * 12  * |  0 0 0  0  2  0  0 1 1 0 | 0 0 0  1  0  0 2  2 0 1 | 0 1 1 0 2
.. .. .. .x    |  0  2 | *  *  *  * 12 |  0 0 0  0  0  0  2 0 1 1 | 0 0 0  0  0  1 0  2 2 1 | 0 0 1 1 2
---------------+-------+---------------+--------------------------+-------------------------+----------
x. .. x. ..    |  4  0 | 2  2  0  0  0 | 12 * *  *  *  *  * * * * | 1 1 0  1  0  0 0  0 0 0 | 1 1 0 1 0
.. o.3x. ..    |  3  0 | 0  3  0  0  0 |  * 8 *  *  *  *  * * * * | 1 0 1  0  0  0 1  0 0 0 | 1 1 0 0 1
.. .. x.3o.    |  3  0 | 0  3  0  0  0 |  * * 8  *  *  *  * * * * | 0 1 1  0  0  0 0  0 1 0 | 1 0 0 1 1
xo .. .. ..&#x |  2  1 | 1  0  2  0  0 |  * * * 24  *  *  * * * * | 0 0 0  1  1  1 0  0 0 0 | 0 1 1 1 0
.. ox .. ..&#x |  1  2 | 0  0  2  1  0 |  * * *  * 24  *  * * * * | 0 0 0  1  0  0 1  1 0 0 | 0 1 1 0 1
.. .. xo ..&#x |  2  1 | 0  1  2  0  0 |  * * *  *  * 24  * * * * | 0 0 0  0  1  0 1  0 1 0 | 0 1 0 1 1
.. .. .. ox&#x |  1  2 | 0  0  2  0  1 |  * * *  *  *  * 24 * * * | 0 0 0  0  0  1 0  1 1 0 | 0 0 1 1 1
.. .x3.o ..    |  0  3 | 0  0  0  3  0 |  * * *  *  *  *  * 4 * * | 0 0 0  0  0  0 2  0 0 1 | 0 1 0 0 2
.. .x .. .x    |  0  4 | 0  0  0  2  2 |  * * *  *  *  *  * * 6 * | 0 0 0  0  0  0 0  2 0 1 | 0 0 1 0 2
.. .. .o3.x    |  0  3 | 0  0  0  0  3 |  * * *  *  *  *  * * * 4 | 0 0 0  0  0  0 0  0 2 1 | 0 0 0 1 2
---------------+-------+---------------+--------------------------+-------------------------+----------
x. o.3x. ..      6  0 | 3  6  0  0  0 |  3 2 0  0  0  0  0 0 0 0 | 4 * *  *  *  * *  * * * | 1 1 0 0 0
x. .. x.3o.      6  0 | 3  6  0  0  0 |  3 0 2  0  0  0  0 0 0 0 | * 4 *  *  *  * *  * * * | 1 0 0 1 0
.. o.3x.3o.      6  0 | 0 12  0  0  0 |  0 4 4  0  0  0  0 0 0 0 | * * 2  *  *  * *  * * * | 1 0 0 0 1
xo ox .. ..&#x   2  2 | 1  0  4  1  0 |  1 0 0  2  2  0  0 0 0 0 | * * * 12  *  * *  * * * | 0 1 1 0 0
xo .. xo ..&#x   4  1 | 2  2  4  0  0 |  0 0 0  2  0  2  0 0 0 0 | * * *  * 12  * *  * * * | 0 1 0 1 0
xo .. .. ox&#x   2  2 | 1  0  4  0  1 |  0 0 0  2  0  0  2 0 0 0 | * * *  *  * 12 *  * * * | 0 0 1 1 0
.. ox3xo ..&#x   3  3 | 0  3  6  3  0 |  0 1 0  0  3  3  0 1 0 0 | * * *  *  *  * 8  * * * | 0 1 0 0 1
.. ox .. ox&#x   1  4 | 0  0  4  2  2 |  0 0 0  0  2  0  2 0 1 0 | * * *  *  *  * * 12 * * | 0 0 1 0 1
.. .. xo3ox&#x   3  3 | 0  3  6  0  3 |  0 0 1  0  0  3  3 0 0 1 | * * *  *  *  * *  * 8 * | 0 0 0 1 1
.. .x3.o3.x      0 12 | 0  0  0 12 12 |  0 0 0  0  0  0  0 4 6 4 | * * *  *  *  * *  * * 1 | 0 0 0 0 2
---------------+-------+---------------+--------------------------+-------------------------+----------
x. o.3x.3o.     12  0 | 6 24  0  0  0 | 12 8 8  0  0  0  0 0 0 0 | 4 4 2  0  0  0 0  0 0 0 | 1 * * * *
xo ox3xo ..&#x   6  3 | 3  6 12  3  0 |  3 2 0  6  6  6  0 1 0 0 | 1 0 0  3  3  0 2  0 0 0 | * 4 * * *
xo ox .. ox&#x   2  4 | 1  0  8  2  2 |  0 0 0  4  4  0  4 0 1 0 | 0 0 0  2  0  2 0  2 0 0 | * * 6 * *
xo .. xo3ox&#x   6  3 | 3  6 12  0  3 |  3 0 2  6  0  6  6 0 0 1 | 0 1 0  0  3  3 0  0 2 0 | * * * 4 *
.. ox3xo3ox&#x   6 12 | 0 12 24 12 12 |  0 4 4  0 12 12 12 4 6 4 | 0 0 1  0  0  0 4  6 4 1 | * * * * 2

oox3xxo3oox&#x   → height(1,2) = 1
                   height(1,3) = height(2,3) = 1/sqrt(2) = 0.707107

o..3o..3o..    | 6 *  * |  4 1  4  0  0  0  0 | 2 2  4  4  2  4  2 0 0  0  0  0 0 0 0 | 1 2 2  2  4  2 2 1 2 0 0 0 0 0 | 1 2 1 2 1 0
.o.3.o.3.o.    | * 6  * |  0 1  0  4  4  0  0 | 0 0  4  4  0  0  0 2 2  2  4  2 0 0 0 | 0 2 2  2  4  2 0 0 0 1 2 1 2 0 | 1 2 1 2 0 1
..o3..o3..o    | * * 12 |  0 0  2  0  2  2  2 | 0 0  0  2  2  1  2 0 0  2  1  2 1 2 1 | 0 0 0  2  1  2 1 2 1 0 1 2 1 1 | 0 1 2 1 1 1
---------------+--------+---------------------+---------------------------------------+--------------------------------+------------
... x.. ...    | 2 0  0 | 12 *  *  *  *  *  * | 1 1  1  0  0  1  0 0 0  0  0  0 0 0 0 | 1 1 1  0  1  0 1 0 1 0 0 0 0 0 | 1 1 0 1 1 0
oo.3oo.3oo.&#x | 1 1  0 |  * 6  *  *  *  *  *  0 0  4  4  0  0  0 0 0  0  0  0 0 0 0 | 0 2 2  2  4  2 0 0 0 0 0 0 0 0 | 1 2 1 2 0 0
o.o3o.o3o.o&#x | 1 0  1 |  * * 24  *  *  *  * | 0 0  0  1  1  1  1 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 |  * *  * 12  *  *  * | 0 0  1  0  0  0  0 1 1  0  1  0 0 0 0 | 0 1 1  0  1  0 0 0 0 1 1 0 1 0 | 1 1 0 1 0 1
.oo3.oo3.oo&#x | 0 1  1 |  * *  *  * 24  *  * | 0 0  0  1  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 |  * *  *  *  * 12  * | 0 0  0  0  1  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 |  * *  *  *  *  * 12 | 0 0  0  0  0  0  1 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 | 4 *  *  *  *  *  * * *  *  *  * * * * | 1 1 0  0  0  0 1 0 0 0 0 0 0 0 | 1 1 0 0 1 0
... x..3o..    | 3 0  0 |  3 0  0  0  0  0  0 | * 4  *  *  *  *  * * *  *  *  * * * * | 1 0 1  0  0  0 0 0 1 0 0 0 0 0 | 1 0 0 1 1 0
... xx. ...&#x | 2 2  0 |  1 2  0  1  0  0  0 | * * 12  *  *  *  * * *  *  *  * * * * | 0 1 1  0  1  0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0
ooo3ooo3ooo&#x | 1 1  1 |  0 1  1  0  1  0  0 | * *  * 24  *  *  * * *  *  *  * * * * | 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  1  0 | * *  *  * 12  *  * * *  *  *  * * * * | 0 0 0  1  0  0 1 1 0 0 0 0 0 0 | 0 1 1 0 1 0
... x.o ...&#x | 2 0  1 |  1 0  2  0  0  0  0 | * *  *  *  * 12  * * *  *  *  * * * * | 0 0 0  0  1  0 1 0 1 0 0 0 0 0 | 0 1 0 1 1 0
... ... o.x&#x | 1 0  2 |  0 0  2  0  0  0  1 | * *  *  *  *  * 12 * *  *  *  * * * * | 0 0 0  0  0  1 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0
.o.3.x. ...    | 0 3  0 |  0 0  0  3  0  0  0 | * *  *  *  *  *  * 4 *  *  *  * * * * | 0 1 0  0  0  0 0 0 0 1 1 0 0 0 | 1 1 0 0 0 1
... .x.3.o.    | 0 3  0 |  0 0  0  3  0  0  0 | * *  *  *  *  *  * * 4  *  *  * * * * | 0 0 1  0  0  0 0 0 0 1 0 0 1 0 | 1 0 0 1 0 1
.ox ... ...&#x | 0 1  2 |  0 0  0  0  2  1  0 | * *  *  *  *  *  * * * 12  *  * * * * | 0 0 0  1  0  0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
... .xo ...&#x | 0 2  1 |  0 0  0  1  2  0  0 | * *  *  *  *  *  * * *  * 12  * * * * | 0 0 0  0  1  0 0 0 0 0 1 0 1 0 | 0 1 0 1 0 1
... ... .ox&#x | 0 1  2 |  0 0  0  0  2  0  1 | * *  *  *  *  *  * * *  *  * 12 * * * | 0 0 0  0  0  1 0 0 0 0 0 1 1 0 | 0 0 1 1 0 1
..x3..o ...    | 0 0  3 |  0 0  0  0  0  3  0 | * *  *  *  *  *  * * *  *  *  * 4 * * | 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  2  2 | * *  *  *  *  *  * * *  *  *  * * 6 * | 0 0 0  0  0  0 0 1 0 0 0 1 0 1 | 0 0 1 0 1 1
... ..o3..x    | 0 0  3 |  0 0  0  0  0  0  3 | * *  *  *  *  *  * * *  *  *  * * * 4 | 0 0 0  0  0  0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
---------------+--------+---------------------+---------------------------------------+--------------------------------+------------
o..3x..3o..     6 0  0 | 12 0  0  0  0  0  0 | 4 4  0  0  0  0  0 0 0  0  0  0 0 0 0 | 1 * *  *  *  * * * * * * * * * | 1 0 0 0 1 0
oo.3xx. ...&#x  3 3  0 |  3 3  0  3  0  0  0 | 1 0  3  0  0  0  0 1 0  0  0  0 0 0 0 | * 4 *  *  *  * * * * * * * * * | 1 1 0 0 0 0
... xx.3oo.&#x  3 3  0 |  3 3  0  3  0  0  0 | 0 1  3  0  0  0  0 0 1  0  0  0 0 0 0 | * * 4  *  *  * * * * * * * * * | 1 0 0 1 0 0
oox ... ...&#x  1 1  2 |  0 1  2  0  2  1  0 | 0 0  0  2  1  0  0 0 0  1  0  0 0 0 0 | * * * 12  *  * * * * * * * * * | 0 1 1 0 0 0
... xxo ...&#x  2 2  1 |  1 2  2  1  2  0  0 | 0 0  1  2  0  1  0 0 0  0  1  0 0 0 0 | * * *  * 12  * * * * * * * * * | 0 1 0 1 0 0
... ... oox&#x  1 1  2 |  0 1  2  0  2  0  1 | 0 0  0  2  0  0  1 0 0  0  0  1 0 0 0 | * * *  *  * 12 * * * * * * * * | 0 0 1 1 0 0
o.x3x.o ...&#x  3 0  3 |  3 0  6  0  0  3  0 | 1 0  0  0  3  3  0 0 0  0  0  0 1 0 0 | * * *  *  *  * 4 * * * * * * * | 0 1 0 0 1 0
o.x ... o.x&#x  1 0  4 |  0 0  4  0  0  2  2 | 0 0  0  0  2  0  2 0 0  0  0  0 0 1 0 | * * *  *  *  * * 6 * * * * * * | 0 0 1 0 1 0
... x.o3o.x&#x  3 0  3 |  3 0  6  0  0  0  3 | 0 1  0  0  0  3  3 0 0  0  0  0 0 0 1 | * * *  *  *  * * * 4 * * * * * | 0 0 0 1 1 0
.o.3.x.3.o.     0 6  0 |  0 0  0 12  0  0  0 | 0 0  0  0  0  0  0 4 4  0  0  0 0 0 0 | * * *  *  *  * * * * 1 * * * * | 1 0 0 0 0 1
.ox3.xo ...&#x  0 3  3 |  0 0  0  3  6  3  0 | 0 0  0  0  0  0  0 1 0  3  3  0 1 0 0 | * * *  *  *  * * * * * 4 * * * | 0 1 0 0 0 1
.ox ... .ox&#x  0 1  4 |  0 0  0  0  4  2  2 | 0 0  0  0  0  0  0 0 0  2  0  2 0 1 0 | * * *  *  *  * * * * * * 6 * * | 0 0 1 0 0 1
... .xo3.ox&#x  0 3  3 |  0 0  0  3  6  0  3 | 0 0  0  0  0  0  0 0 1  0  3  3 0 0 1 | * * *  *  *  * * * * * * * 4 * | 0 0 0 1 0 1
..x3..o3..x     0 0 12 |  0 0  0  0  0 12 12 | 0 0  0  0  0  0  0 0 0  0  0  0 4 6 4 | * * *  *  *  * * * * * * * * 1 | 0 0 0 0 1 1
---------------+--------+---------------------+---------------------------------------+--------------------------------+------------
oo.3xx.3oo.&#x  6 6  0 | 12 6  0 12  0  0  0 | 4 4 12  0  0  0  0 4 4  0  0  0 0 0 0 | 1 4 4  0  0  0 0 0 0 1 0 0 0 0 | 1 * * * * *
oox3xxo ...&#x  3 3  3 |  3 3  6  3  6  3  0 | 1 0  3  6  3  3  0 1 0  3  3  0 1 0 0 | 0 1 0  3  3  0 1 0 0 0 1 0 0 0 | * 4 * * * *
oox ... oox&#x  1 1  4 |  0 1  4  0  4  2  2 | 0 0  0  4  2  0  2 0 0  2  0  2 0 1 0 | 0 0 0  2  0  2 0 1 0 0 0 1 0 0 | * * 6 * * *
... xxo3oox&#x  3 3  3 |  3 3  6  3  6  0  3 | 0 1  3  6  0  3  3 0 1  0  3  3 0 0 1 | 0 0 1  0  3  3 0 0 1 0 0 0 1 0 | * * * 4 * *
o.x3x.o3o.x&#x  6 0 12 | 12 0 24  0  0 12 12 | 4 4  0  0 12 12 12 0 0  0  0  0 4 6 4 | 1 0 0  0  0  0 4 6 4 0 0 0 0 1 | * * * * 1 *
.ox3.xo3.ox&#x  0 6 12 |  0 0  0 12 24 12 12 | 0 0  0  0  0  0  0 4 4 12 12 12 4 6 4 | 0 0 0  0  0  0 0 0 0 1 4 6 4 1 | * * * * * 1

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