Acronym pacop
Name partially Stott contracted octagonal prism
Vertex figure [42,h], [42,H]
Lace city
in approx. ASCII-art 
  x   x  
x       x
  x   x  

o q   q o
         
o q   q o

x w x
     
x w x
Dihedral angles
  • between {4} and {4} (at H):   135°
  • between {4} and {4} (at h):   90°
  • between {4} and {(h,H,H)2}:   90°
Face vector 12, 18, 8
Confer
uniform variant:
hip   op  
general polytopal classes:
partial Stott expansions  

The non-regular hexagons {(h,H,H)2} are diagonally elongated squares. Its vertex angles are h = 90° resp. H = 135°.


Incidence matrix according to Dynkin symbol

xxx xwx&#xt   → both heights = 1/sqrt(2) = 0.707107
({4} || pseudo (x,w)-{4} || {4})

o.. o..     | 4 * * | 1 1 1 0 0 0 0 | 1 1 1 0 0
.o. .o.     | * 4 * | 0 0 1 1 1 0 0 | 0 1 1 1 0
..o ..o     | * * 4 | 0 0 0 0 1 1 1 | 0 0 1 1 1
------------+-------+---------------+----------
x.. ...     | 2 0 0 | 2 * * * * * * | 1 1 0 0 0
... x..     | 2 0 0 | * 2 * * * * * | 1 0 1 0 0
oo. oo.&#x  | 1 1 0 | * * 4 * * * * | 0 1 1 0 0
.x. ...     | 0 2 0 | * * * 2 * * * | 0 1 0 1 0
.oo .oo&#x  | 0 1 1 | * * * * 4 * * | 0 0 1 1 0
..x ...     | 0 0 2 | * * * * * 2 * | 0 0 0 1 1
... ..x     | 0 0 2 | * * * * * * 2 | 0 0 1 0 1
------------+-------+---------------+----------
x.. x..     | 4 0 0 | 2 2 0 0 0 0 0 | 1 * * * *
xx. ...&#x  | 2 2 0 | 1 0 2 1 0 0 0 | * 2 * * *
... xwx&#xt | 2 2 2 | 0 1 2 0 2 0 1 | * * 2 * *  {(h,H,H)2}
.xx ...&#x  | 0 2 2 | 0 0 0 1 2 1 0 | * * * 2 *
..x ..x     | 0 0 4 | 0 0 0 0 0 2 2 | * * * * 1

or
o.. o..     & | 8 * | 1 1 1 0 | 1 1 1
.o. .o.       | * 4 | 0 0 2 1 | 0 2 1
--------------+-----+---------+------
x.. ...     & | 2 0 | 4 * * * | 1 1 0
... x..     & | 2 0 | * 4 * * | 1 0 1
oo. oo.&#x  & | 1 1 | * * 8 * | 0 1 1
.x. ...       | 0 2 | * * * 2 | 0 2 0
--------------+-----+---------+------
x.. x..     & | 4 0 | 2 2 0 0 | 2 * *
xx. ...&#x  & | 2 2 | 1 0 2 1 | * 4 *
... xwx&#xt   | 4 2 | 0 2 4 0 | * * 2  {(h,H,H)2}


xxxx oqqo&#xt   → outer heights = 1/sqrt(2) = 0.707107
                  inner height = 1
(line || pseudo (x,q)-{4} || pseudo (x,q)-{4} || line)

o... o...     | 2 * * * | 1 2 0 0 0 0 0 | 2 1 0 0
.o.. .o..     | * 4 * * | 0 1 1 1 0 0 0 | 1 1 1 0
..o. ..o.     | * * 4 * | 0 0 0 1 1 1 0 | 0 1 1 1
...o ...o     | * * * 2 | 0 0 0 0 0 2 1 | 0 1 0 2
--------------+---------+---------------+--------
x... ....     | 2 0 0 0 | 1 * * * * * * | 2 0 0 0
oo.. oo..&#x  | 1 1 0 0 | * 4 * * * * * | 1 1 0 0
.x.. ....     | 0 2 0 0 | * * 2 * * * * | 1 0 1 0
.oo. .oo.&#x  | 0 1 1 0 | * * * 4 * * * | 0 1 1 0
..x. ....     | 0 0 2 0 | * * * * 2 * * | 0 0 1 1
..oo ..oo&#x  | 0 0 1 1 | * * * * * 4 * | 0 1 0 1
...x ....     | 0 0 0 2 | * * * * * * 1 | 0 0 0 2
--------------+---------+---------------+--------
xx.. ....&#x  | 2 2 0 0 | 1 2 1 0 0 0 0 | 2 * * *
.... oqqo&#xt | 1 2 2 1 | 0 2 0 2 0 2 0 | * 2 * *  {(h,H,H)2}
.xx. ....&#x  | 0 2 2 0 | 0 0 1 2 1 0 0 | * * 2 *
..xx ....&#x  | 0 0 2 2 | 0 0 0 0 1 2 1 | * * * 2

or
o... o...     & | 4 * | 1 2 0 0 | 2 1 0
.o.. .o..     & | * 8 | 0 1 1 1 | 1 1 1
----------------+-----+---------+------
x... ....     & | 2 0 | 2 * * * | 2 0 0
oo.. oo..&#x  & | 1 1 | * 8 * * | 1 1 0
.x.. ....     & | 0 2 | * * 4 * | 1 0 1
.oo. .oo.&#x    | 0 2 | * * * 4 | 0 1 1
----------------+-----+---------+------
xx.. ....&#x  & | 2 2 | 1 2 1 0 | 4 * *
.... oqqo&#xt   | 2 4 | 0 4 0 2 | * 2 *  {(h,H,H)2}
.xx. ....&#x    | 0 4 | 0 0 2 2 | * * 2


wx oq xx&#zx   → height = 0

o. o. o.     | 4 * | 1 2 0 0 | 1 2 0
.o .o .o     | * 8 | 0 1 1 1 | 1 1 1
-------------+-----+---------+------
.. .. x.     | 2 0 | 2 * * * | 0 2 0
oo oo oo&#x  | 1 1 | * 8 * * | 1 1 0
.x .. ..     | 0 2 | * * 4 * | 1 0 1
.. .. .x     | 0 2 | * * * 4 | 0 1 1
-------------+-----+---------+------
wx oq ..&#zx | 2 4 | 0 4 2 0 | 2 * *  {(h,H,H)2}
.. .. xx&#x  | 2 2 | 1 2 0 1 | * 4 *
.x .. .x     | 0 4 | 0 0 2 2 | * * 2


xxx4oso&#xt

      o..4o..       | 4 * * | 1 1 1 0 0 0 0 | 1 1 0 0 1
demi( .o.4.o.     ) | * 4 * | 0 0 1 1 1 0 0 | 0 1 1 0 1
      ..o4..o       | * * 4 | 0 0 0 0 1 1 1 | 0 0 1 1 1
--------------------+-------+---------------+----------
demi( x.. ...     ) | 2 0 0 | 2 * * * * * * | 1 1 0 0 0
demi( x.. ...     ) | 2 0 0 | * 2 * * * * * | 1 0 0 0 1
demi( oo.4oo.&#x  ) | 1 1 0 | * * 4 * * * * | 0 1 0 0 1
demi( .x. ...     ) | 0 2 0 | * * * 2 * * * | 0 1 1 0 0
demi( .oo4.oo&#x  ) | 0 1 1 | * * * * 4 * * | 0 0 1 0 1
demi( ..x ...     ) | 0 0 2 | * * * * * 2 * | 0 0 1 1 0
demi( ..x ...     ) | 0 0 2 | * * * * * * 2 | 0 0 0 1 1
--------------------+-------+---------------+----------
      x..4o..       | 4 0 0 | 2 2 0 0 0 0 0 | 1 * * * *
demi( xx. ...&#x  ) | 2 2 0 | 1 0 2 1 0 0 0 | * 2 * * *
demi( .xx ...&#x  ) | 0 2 2 | 0 0 0 1 2 1 0 | * * 2 * *
      ..x4..o       | 0 0 4 | 0 0 0 0 0 2 2 | * * * 1 *
sefa( xxx4oso&#xt ) | 2 2 2 | 0 1 2 0 2 0 1 | * * * * 2  {(h,H,H)2}

starting figure: xxx4oxo&#xt

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