Acronym opepy
Name octahedral-prismatic pyramid,
vertex pyramid of rectified triacontiditeron
Circumradius 1
Lace city
in approx. ASCII-art
o   O       
            O = x3o4o = oct
O           o = o3o4o = point
o   t       t = o3x x = oct
            T = x3o x = oct
T           o = o3o o = point
Confer
uniform relative:
rat  
related segmentotera:
squippyippy  
general polytopal classes:
segmentotera   lace simplices  

Incidence matrix according to Dynkin symbol

ox ox3oo4oo&#x   → height = 1/2
(pt || ope)

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

ox oo3ox3oo&#x   → height = 1/2
(pt || ope)

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

oxx3ooo4ooo&#x   → height(1,2) = height(1,3) = 1/sqrt(2) = 0.707107
                   height(2,3) = 1

... 

ooo3oxx3ooo&#x   → height(1,2) = height(1,3) = 1/sqrt(2) = 0.707107
                   height(2,3) = 1

o..3o..3o..    | 1 * *  6 6  0 0  0 | 12 6 12 0 0  0 0 0 | 4 4 12 4 4 0 0 0 0 | 1 4 4 1 0
.o.3.o.3.o.    | * 6 * | 1 0  4 1  0 |  4 1  0 2 2  4 0 0 | 2 2  4 0 0 1 2 2 0 | 1 2 2 0 1
..o3..o3..o    | * * 6 | 0 1  0 1  4 |  0 1  4 0 0  4 2 2 | 0 0  4 2 2 0 2 2 1 | 0 2 2 1 1
---------------+-------+-------------+--------------------+--------------------+----------
oo.3oo.3oo.&#x | 1 1 0 | 6 *  * *  *   4 1  0 0 0  0 0 0 | 2 2  4 0 0 0 0 0 0 | 1 2 2 0 0
o.o3o.o3o.o&#x | 1 0 1 | * 6  * *  *   0 1  4 0 0  0 0 0 | 0 0  4 2 2 0 0 0 0 | 0 2 2 1 0
... .x. ...    | 0 2 0 | * * 12 *  * |  1 0  0 1 1  1 0 0 | 1 1  1 0 0 1 1 1 0 | 1 1 1 0 1
.oo3.oo3.oo&#x | 0 1 1 | * *  * 6  * |  0 1  0 0 0  4 0 0 | 0 0  4 0 0 0 2 2 0 | 0 2 2 0 1
... ..x ...    | 0 0 2 | * *  * * 12 |  0 0  1 0 0  1 1 1 | 0 0  1 1 1 0 1 1 1 | 0 1 1 1 1
---------------+-------+-------------+--------------------+--------------------+----------
... ox. ...&#x | 1 2 0 | 2 0  1 0  0 | 12 *  * * *  * * * | 1 1  1 0 0 0 0 0 0 | 1 1 1 0 0
ooo3ooo3ooo&#x | 1 1 1 | 1 1  0 1  0 |  * 6  * * *  * * * | 0 0  4 0 0 0 0 0 0 | 0 2 2 0 0
... o.x ...&#x | 1 0 2 | 0 2  0 0  1 |  * * 12 * *  * * * | 0 0  1 1 1 0 0 0 0 | 0 1 1 1 0
.o.3.x. ...    | 0 3 0 | 0 0  3 0  0 |  * *  * 4 *  * * * | 1 0  0 0 0 1 1 0 0 | 1 1 0 0 1
... .x.3.o.    | 0 3 0 | 0 0  3 0  0 |  * *  * * 4  * * * | 0 1  0 0 0 1 0 1 0 | 1 0 1 0 1
... .xx ...&#x | 0 2 2 | 0 0  1 2  1 |  * *  * * * 12 * * | 0 0  1 0 0 0 1 1 0 | 0 1 1 0 1
..o3..x ...    | 0 0 3 | 0 0  0 0  3 |  * *  * * *  * 4 * | 0 0  0 1 0 0 1 0 1 | 0 1 0 1 1
... ..x3..o    | 0 0 3 | 0 0  0 0  3 |  * *  * * *  * * 4 | 0 0  0 0 1 0 0 1 1 | 0 0 1 1 1
---------------+-------+-------------+--------------------+--------------------+----------
oo.3ox. ...&#x  1 3 0 | 3 0  3 0  0 |  3 0  0 1 0  0 0 0 | 4 *  * * * * * * * | 1 1 0 0 0
... ox.3oo.&#x  1 3 0 | 3 0  3 0  0 |  3 0  0 0 1  0 0 0 | * 4  * * * * * * * | 1 0 1 0 0
... oxx ...&#x  1 2 2 | 2 2  1 2  1 |  1 2  1 0 0  1 0 0 | * * 12 * * * * * * | 0 1 1 0 0
o.o3o.x ...&#x  1 0 3 | 0 3  0 0  3 |  0 0  3 0 0  0 1 0 | * *  * 4 * * * * * | 0 1 0 1 0
... o.x3o.o&#x  1 0 3 | 0 3  0 0  3 |  0 0  3 0 0  0 0 1 | * *  * * 4 * * * * | 0 0 1 1 0
.o.3.x.3.o.     0 6 0 | 0 0 12 0  0 |  0 0  0 4 4  0 0 0 | * *  * * * 1 * * * | 1 0 0 0 1
.oo3.xx ...&#x  0 3 3 | 0 0  3 3  3 |  0 0  0 1 0  3 1 0 | * *  * * * * 4 * * | 0 1 0 0 1
... .xx3.oo&#x  0 3 3 | 0 0  3 3  3 |  0 0  0 0 1  3 0 1 | * *  * * * * * 4 * | 0 0 1 0 1
..o3..x3..o     0 0 6 | 0 0  0 0 12 |  0 0  0 0 0  0 4 4 | * *  * * * * * * 1 | 0 0 0 1 1
---------------+-------+-------------+--------------------+--------------------+----------
oo.3ox.3oo.&#x  1 6 0 | 6 0 12 0  0 | 12 0  0 4 4  0 0 0 | 4 4  0 0 0 1 0 0 0 | 1 * * * *
ooo3oxx ...&#x  1 3 3 | 3 3  3 3  3 |  3 3  3 1 0  3 1 0 | 1 0  3 1 0 0 1 0 0 | * 4 * * *
... oxx3ooo&#x  1 3 3 | 3 3  3 3  3 |  3 3  3 0 1  3 0 1 | 0 1  3 0 1 0 0 1 0 | * * 4 * *
o.o3o.x3o.o&#x  1 0 6 | 0 6  0 0 12 |  0 0 12 0 0  0 4 4 | 0 0  0 4 4 0 0 0 1 | * * * 1 *
.oo3.xx3.oo&#x  0 6 6 | 0 0 12 6 12 |  0 0  0 4 4 12 4 4 | 0 0  0 0 0 1 4 4 1 | * * * * 1

oxx oox3oxo&#x   → height(1,2) = height(1,3) = sqrt(5/12) = 0.645497
                   height(2,3) = sqrt(2/3) = 0.816497
                   height(1,23) = 1/2

o.. o..3o..    | 1 * *  6 6 0 0  0 0 0 | 3 6 12 3 6 0 0 0 0 0 0 0 | 3 2 6 6 6 3 2 0 0 0 0 0 | 1 3 3 2 1 0
.o. .o.3.o.    | * 6 * | 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 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
---------------+-------+----------------+--------------------------+-------------------------+------------
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
---------------+-------+----------------+--------------------------+-------------------------+------------
ox. ... ...&#x | 1 2 0 | 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 | 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 | 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
o.x ... ...&#x | 1 0 2 | 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 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 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 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 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  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 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 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 3 | * *  * * * * * * * * * 2 | 0 0 0 0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
---------------+-------+----------------+--------------------------+-------------------------+------------
ox. ... ox.&#x  1 4 0 | 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 | 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
oxx ... ...&#x  1 2 2 | 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 | 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 | 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
o.x o.x ...&#x  1 0 4 | 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 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 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 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 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 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 3 6 | 0 0  0 0 0 0 0 0 0 0 3 2 | * * * * * * * * * * * 1 | 0 0 0 0 1 1
---------------+-------+----------------+--------------------------+-------------------------+------------
ox. oo.3ox.&#x  1 6 0 | 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 * * * * *
oxx oox ...&#x  1 2 4 | 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 * * * *
oxx ... oxo&#x  1 4 2 | 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 | 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 * *
o.x o.x3o.o&#x  1 0 6 | 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 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

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