Acronym octpy || octaco
Name 1/4-lune of rectified triacontiditeron (but not coahex),
octahedron-pyramid atop octhedron-first-rotunda-of-icositetrachoron
Circumradius 1
Lace city
in approx. ASCII-art
             _ +-------- o o3o4o (pt)
         _ -    _ +----- x x3o4o (ope)
     _ -    _ -    _ +-- o o3x4o (co)

o3o4o  x3o4o		-- ox3oo4oo&#x (octpy)
            
            
            
x3o4o  o3x4o		-- xo3ox4oo&#x (octaco)
Confer
uniform relative:
rat  
related segmentotera:
opepy   opeaco   coahex  
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

oxo oxo3oox4ooo&#xt   → both heights = 1/2
(pt || pseudo ope || co)

o.. o..3o..4o..     | 1  *  *  12 0  0  0  0 | 6 24  0  0  0  0 0 0 | 12 16 0  0  0  0 0 | 8 2 0 0
.o. .o.3.o.4.o.     | * 12  * |  1 1  4  4  0 | 1  4  4  4  4  4 0 0 |  4  4 1  4  4  1 0 | 4 1 1 1
..o ..o3..o4..o     | *  * 12 |  0 0  0  4  4 | 0  0  0  2  2  8 2 2 |  1  0 0  4  4  4 1 | 2 0 2 2
--------------------+---------+---------------+----------------------+--------------------+--------
oo. oo.3oo.4oo.&#x  | 1  1  0 | 12 *  *  *  *  1  4  0  0  0  0 0 0 |  4  4 0  0  0  0 0 | 4 1 0 0
.x. ... ... ...     | 0  2  0 |  * 6  *  *  *  1  0  0  4  0  0 0 0 |  4  0 0  4  0  0 0 | 4 0 1 0
... .x. ... ...     | 0  2  0 |  * * 24  *  * | 0  1  2  0  1  0 0 0 |  1  2 1  0  2  0 0 | 2 1 0 1
.oo .oo3.oo4.oo&#x  | 0  1  1 |  * *  * 48  * | 0  0  0  1  1  2 0 0 |  1  0 0  2  2  1 0 | 2 0 1 1
... ... ..x ...     | 0  0  2 |  * *  *  * 24 | 0  0  0  0  0  2 1 1 |  0  0 0  1  2  2 1 | 1 0 1 2
--------------------+---------+---------------+----------------------+--------------------+--------
ox. ... ... ...&#x  | 1  2  0 |  2 1  0  0  0 | 6  *  *  *  *  * * * |  4  0 0  0  0  0 0 | 4 0 0 0
... ox. ... ...&#x  | 1  2  0 |  2 0  1  0  0 | * 24  *  *  *  * * * |  1  2 0  0  0  0 0 | 2 1 0 0
... .x.3.o. ...     | 0  3  0 |  0 0  3  0  0 | *  * 16  *  *  * * * |  0  1 1  0  1  0 0 | 1 1 0 1
.xo ... ... ...&#x  | 0  2  1 |  0 1  0  2  0 | *  *  * 24  *  * * * |  1  0 0  2  0  0 0 | 2 0 1 0
... .xo ... ...&#x  | 0  2  1 |  0 0  1  2  0 | *  *  *  * 24  * * * |  1  0 0  0  2  0 0 | 2 0 0 1
... ... .ox ...&#x  | 0  1  2 |  0 0  0  2  1 | *  *  *  *  * 48 * * |  0  0 0  1  1  1 0 | 1 0 1 1
... ..o3..x ...     | 0  0  3 |  0 0  0  0  3 | *  *  *  *  *  * 8 * |  0  0 0  0  2  0 1 | 1 0 0 2
... ... ..x4..o     | 0  0  4 |  0 0  0  0  4 | *  *  *  *  *  * * 6 |  0  0 0  0  0  2 1 | 0 0 1 2
--------------------+---------+---------------+----------------------+--------------------+--------
oxo oxo ... ...&#xt  1  4  1 |  4 2  2  4  0 | 2  2  0  2  2  0 0 0 | 12  * *  *  *  * * | 2 0 0 0
... ox.3oo. ...&#x   1  3  0 |  3 0  3  0  0 | 0  3  1  0  0  0 0 0 |  * 16 *  *  *  * * | 1 1 0 0
... .x.3.o.4.o.      0  6  0 |  0 0 12  0  0 | 0  0  8  0  0  0 0 0 |  *  * 2  *  *  * * | 0 1 0 1
.xo ... .ox ...&#x   0  2  2 |  0 1  0  4  1 | 0  0  0  2  0  2 0 0 |  *  * * 24  *  * * | 1 0 1 0
... .xo3.ox ...&#x   0  3  3 |  0 0  3  6  3 | 0  0  1  0  3  3 1 0 |  *  * *  * 16  * * | 1 0 0 1
... ... .ox4.oo&#x   0  1  4 |  0 0  0  4  4 | 0  0  0  0  0  4 0 1 |  *  * *  *  * 12 * | 0 0 1 1
... ..o3..x4.o       0  0 12 |  0 0  0  0 24 | 0  0  0  0  0  0 8 6 |  *  * *  *  *  * 1 | 0 0 0 2
--------------------+---------+---------------+----------------------+--------------------+--------
oxo oxo3oox ...&#xt  1  6  3 |  6 3  6 12  3 | 3  6  2  6  6  6 1 0 |  3  2 0  3  2  0 0 | 8 * * *
... ox.3oo.4oo.&#x   1  6  0 |  6 0 12  0  0 | 0 12  8  0  0  0 0 0 |  0  8 1  0  0  0 0 | * 2 * *
.xo ... .ox4.oo&#x   0  2  4 |  0 1  0  8  4 | 0  0  0  4  0  8 0 1 |  0  0 0  4  0  2 0 | * * 6 *
... .xo3.ox4.oo&#x   0  6 12 |  0 0 12 24 24 | 0  0  8  0 12 24 8 6 |  0  0 1  0  8  6 1 | * * * 2

ox3oo4oo&#x || xo3ox4oo&#x   → height = 1/sqrt(2) = 0.707107
(octpy || octaco)

o.3o.4o.       .. .. ..    | 1 * *  *  6 6  0 0  0  0  0  0 | 12 6 12 0  0  0  0 0  0  0 0 0 | 8 12 8 0 0  0 0 0 0 0 0 | 1 8 1 0 0 0
.o3.o4.o       .. .. ..    | * 6 *  * | 1 0  4 1  4  0  0  0 |  4 1  0 4  4  4  4 0  0  0 0 0 | 4  4 0 1 4  4 1 0 0 0 0 | 1 4 0 1 1 0
.. .. ..       o.3o.4o.    | * * 6  * | 0 1  0 1  0  4  4  0 |  0 1  4 0  0  4  0 4  4  4 0 0 | 0  4 4 0 0  4 0 1 4 1 0 | 0 4 1 0 1 1
.. .. ..       .o3.o4.o    | * * * 12 | 0 0  0 0  2  0  2  4 |  0 0  0 0  1  2  4 0  1  4 2 2 | 0  1 0 0 2  4 2 0 2 2 1 | 0 2 0 1 2 1
---------------------------+----------+----------------------+--------------------------------+-------------------------+------------
oo3oo4oo&#x    .. .. ..    | 1 1 0  0 | 6 *  * *  *  *  *  *   4 1  0 0  0  0  0 0  0  0 0 0 | 4  4 0 0 0  0 0 0 0 0 0 | 1 4 0 0 0 0
o.3o.4o.    || o.3o.4o.    | 1 0 1  0 | * 6  * *  *  *  *  *   0 1  4 0  0  0  0 0  0  0 0 0 | 0  4 4 0 0  0 0 0 0 0 0 | 0 4 1 0 0 0
.x .. ..       .. .. ..    | 0 2 0  0 | * * 12 *  *  *  *  * |  1 0  0 2  1  0  0 0  0  0 0 0 | 2  1 0 1 2  0 0 0 0 0 0 | 1 2 0 1 0 0
.o3.o4.o    || o.3o.4o.    | 0 1 1  0 | * *  * 6  *  *  *  *   0 1  0 0  0  4  0 0  0  0 0 0 | 0  4 0 0 0  4 0 0 0 0 0 | 0 4 0 0 1 0
.o3.o4.o    || .o3.o4.o    | 0 1 0  1 | * *  * * 24  *  *  * |  0 0  0 0  1  1  2 0  0  0 0 0 | 0  1 0 0 2  2 1 0 0 0 0 | 0 2 0 1 1 0
.. .. ..       x. .. ..    | 0 0 2  0 | * *  * *  * 12  *  * |  0 0  1 0  0  0  0 2  1  0 0 0 | 0  1 2 0 0  0 0 1 2 0 0 | 0 2 1 0 0 1
.. .. ..       oo3oo4oo&#x | 0 0 1  1 | * *  * *  *  * 24  * |  0 0  0 0  0  1  0 0  1  2 0 0 | 0  1 0 0 0  2 0 0 2 1 0 | 0 2 0 0 1 1
.. .. ..       .. .x ..    | 0 0 0  2 | * *  * *  *  *  * 24 |  0 0  0 0  0  0  1 0  0  1 1 1 | 0  0 0 0 1  1 1 0 1 1 1 | 0 1 0 1 1 1
---------------------------+----------+----------------------+--------------------------------+-------------------------+------------
ox .. ..&#x    .. .. ..    | 1 2 0  0 | 2 0  1 0  0  0  0  0 | 12 *  * *  *  *  * *  *  * * * | 2  1 0 0 0  0 0 0 0 0 0 | 1 2 0 0 0 0
oo3oo4oo&#x || o.3o.4o.    | 1 1 1  0 | 1 1  0 1  0  0  0  0 |  * 6  * *  *  *  * *  *  * * * | 0  4 0 0 0  0 0 0 0 0 0 | 0 4 0 0 0 0
o.3o.4o.    || x. .. ..    | 1 0 2  0 | 0 2  0 0  0  1  0  0 |  * * 12 *  *  *  * *  *  * * * | 0  1 2 0 0  0 0 0 0 0 0 | 0 2 1 0 0 0
.x3.o ..       .. .. ..    | 0 3 0  0 | 0 0  3 0  0  0  0  0 |  * *  * 8  *  *  * *  *  * * * | 1  0 0 1 1  0 0 0 0 0 0 | 1 1 0 1 0 0
.x .. ..    || .o3.o4.o    | 0 2 0  1 | 0 0  1 0  2  0  0  0 |  * *  * * 12  *  * *  *  * * * | 0  1 0 0 2  0 0 0 0 0 0 | 0 2 0 1 0 0
.o3.o4.o    || oo3oo4oo&#x | 0 1 1  1 | 0 0  0 1  1  0  1  0 |  * *  * *  * 24  * *  *  * * * | 0  1 0 0 0  2 0 0 0 0 0 | 0 2 0 0 1 0
.o3.o4.o    || .. .x ..    | 0 1 0  2 | 0 0  0 0  2  0  0  1 |  * *  * *  *  * 24 *  *  * * * | 0  0 0 0 1  1 1 0 0 0 0 | 0 1 0 1 1 0
.. .. ..       x.3o. ..    | 0 0 3  0 | 0 0  0 0  0  3  0  0 |  * *  * *  *  *  * 8  *  * * * | 0  0 1 0 0  0 0 1 1 0 0 | 0 1 1 0 0 1
.. .. ..       xo .. ..&#x | 0 0 2  1 | 0 0  0 0  0  1  2  0 |  * *  * *  *  *  * * 12  * * * | 0  1 0 0 0  0 0 0 2 0 0 | 0 2 0 0 0 1
.. .. ..       .. ox ..&#x | 0 0 1  2 | 0 0  0 0  0  0  2  1 |  * *  * *  *  *  * *  * 24 * * | 0  0 0 0 0  1 0 0 1 1 0 | 0 1 0 0 1 1
.. .. ..       .o3.x ..    | 0 0 0  3 | 0 0  0 0  0  0  0  3 |  * *  * *  *  *  * *  *  * 8 * | 0  0 0 0 1  0 0 0 1 0 1 | 0 1 0 1 0 1
.. .. ..       .. .x4.o    | 0 0 0  4 | 0 0  0 0  0  0  0  4 |  * *  * *  *  *  * *  *  * * 6 | 0  0 0 0 0  0 1 0 0 1 1 | 0 0 0 1 1 1
---------------------------+----------+----------------------+--------------------------------+-------------------------+------------
ox3oo ..&#x    .. .. ..     1 3 0  0 | 3 0  3 0  0  0  0  0 |  3 0  0 1  0  0  0 0  0  0 0 0 | 8  * * * *  * * * * * * | 1 1 0 0 0 0
ox .. ..&#x || xo .. ..&#x  1 2 2  1 | 2 2  1 2  2  1  2  0 |  1 2  1 0  1  2  0 0  1  0 0 0 | * 12 * * *  * * * * * * | 0 2 0 0 0 0
o.3o.4o.    || x.3o. ..     1 0 3  0 | 0 3  0 0  0  3  0  0 |  0 0  3 0  0  0  0 1  0  0 0 0 | *  * 8 * *  * * * * * * | 0 1 1 0 0 0
.x3.o4.o       .. .. ..     0 6 0  0 | 0 0 12 0  0  0  0  0 |  0 0  0 8  0  0  0 0  0  0 0 0 | *  * * 1 *  * * * * * * | 1 0 0 1 0 0
.x3.o ..    || .o3.x ..     0 3 0  3 | 0 0  3 0  6  0  0  3 |  0 0  0 1  3  0  3 0  0  0 1 0 | *  * * * 8  * * * * * * | 0 1 0 1 0 0
.o3.o4.o    || .. ox ..&#x  0 1 1  2 | 0 0  0 1  2  0  2  1 |  0 0  0 0  0  2  1 0  0  1 0 0 | *  * * * * 24 * * * * * | 0 1 0 0 1 0
.o3.o4.o    || .. .x4.o     0 1 0  4 | 0 0  0 0  4  0  0  4 |  0 0  0 0  0  0  4 0  0  0 0 1 | *  * * * *  * 6 * * * * | 0 0 0 1 1 0
.. .. ..       x.3o.4o.     0 0 6  0 | 0 0  0 0  0 12  0  0 |  0 0  0 0  0  0  0 8  0  0 0 0 | *  * * * *  * * 1 * * * | 0 0 1 0 0 1
.. .. ..       xo3ox ..&#x  0 0 3  3 | 0 0  0 0  0  3  6  3 |  0 0  0 0  0  0  0 1  3  3 1 0 | *  * * * *  * * * 8 * * | 0 1 0 0 0 1
.. .. ..       .. ox4oo&#x  0 0 1  4 | 0 0  0 0  0  0  4  4 |  0 0  0 0  0  0  0 0  0  4 0 1 | *  * * * *  * * * * 6 * | 0 0 0 0 1 1
.. .. ..       .o3.x4.o     0 0 0 12 | 0 0  0 0  0  0  0 24 |  0 0  0 0  0  0  0 0  0  0 8 6 | *  * * * *  * * * * * 1 | 0 0 0 1 0 1
---------------------------+----------+----------------------+--------------------------------+-------------------------+------------
ox3oo4oo&#x    .. .. ..     1 6 0  0 | 6 0 12 0  0  0  0  0 | 12 0  0 8  0  0  0 0  0  0 0 0 | 8  0 0 1 0  0 0 0 0 0 0 | 1 * * * * *
ox3oo ..&#x || xo3ox ..&#x  1 3 3  3 | 3 3  3 3  6  3  6  3 |  3 3  3 1  3  6  3 1  3  3 1 0 | 1  3 1 0 1  3 0 0 1 0 0 | * 8 * * * *
o.3o.4o.    || x.3o.4o.     1 0 6  0 | 0 6  0 0  0 12  0  0 |  0 0 12 0  0  0  0 8  0  0 0 0 | 0  0 8 0 0  0 0 1 0 0 0 | * * 1 * * *
.x3.o4.o    || .o3.x4.o     0 6 0 12 | 0 0 12 0 24  0  0 24 |  0 0  0 8 12  0 24 0  0  0 8 6 | 0  0 0 1 8  0 6 0 0 0 1 | * * * 1 * *
.o3.o4.o    || .. ox4oo&#x  0 1 1  4 | 0 0  0 1  4  0  4  4 |  0 0  0 0  0  4  4 0  0  4 0 1 | 0  0 0 0 0  4 1 0 0 1 0 | * * * * 6 *
.. .. ..       xo3ox4oo&#x  0 0 6 12 | 0 0  0 0  0 12 24 24 |  0 0  0 0  0  0  0 8 12 24 8 6 | 0  0 0 0 0  0 0 1 8 6 1 | * * * * * 1

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