Acronym pac girco
Name partially (mono-)contracted great rhombicuboctahedron
 
Circumradius ...
Vertex figure [4,6,8], [4,6,H], [h,6,6]
Lace city
in approx. ASCII-art
  o q  q o  
o   Q  Q   o
q Q      Q q	(Q=2q)
            
q Q      Q q
o   Q  Q   o
  o q  q o  
  x w  w x  
x   W  W   x	(W=u+w)
w W      W w
x   W  W   x
  x w  w x  
Dihedral angles
(at margins)
  • between {4} and {6}:   arccos(-sqrt(2/3)) = 144.735610°
  • between {4} and {8}:   135°
  • between {4} and {(h,H,H)2}:   135°
  • between {(h,H,H)2} and {6}:   arccos(-1/sqrt(3)) = 125.264390°
  • between {6} and {6}:   arccos(-1/3) = 109.471221°
Confer
uniform relative:
girco  
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

xuxux4xxwxx&#xt   → all heights = 1/sqrt(2) = 0.707107
({8} || pseudo (u,x)-{8} || pseudo (x,w)-{8} || pseudo (u,x)-{8} || {8})

o....4o....     | 8 * * * * | 1 1 1 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0  [4,6,8]
.o...4.o...     | * 8 * * * | 0 0 1 1 1 0 0 0 0 0 0 | 0 1 1 1 0 0 0  [4,6,H]
..o..4..o..     | * * 8 * * | 0 0 0 0 1 1 1 0 0 0 0 | 0 1 0 1 1 0 0  [h,6,6]
...o.4...o.     | * * * 8 * | 0 0 0 0 0 0 1 1 1 0 0 | 0 0 0 1 1 1 0  [4,6,H]
....o4....o     | * * * * 8 | 0 0 0 0 0 0 0 0 1 1 1 | 0 0 0 0 1 1 1  [4,6,8]
----------------+-----------+-----------------------+--------------
x.... .....     | 2 0 0 0 0 | 4 * * * * * * * * * * | 1 1 0 0 0 0 0
..... x....     | 2 0 0 0 0 | * 4 * * * * * * * * * | 1 0 1 0 0 0 0
oo...4oo...&#x  | 1 1 0 0 0 | * * 8 * * * * * * * * | 0 1 1 0 0 0 0
..... .x...     | 0 2 0 0 0 | * * * 4 * * * * * * * | 0 0 1 1 0 0 0
.oo..4.oo..&#x  | 0 1 1 0 0 | * * * * 8 * * * * * * | 0 1 0 1 0 0 0
..x.. .....     | 0 0 2 0 0 | * * * * * 4 * * * * * | 0 1 0 0 1 0 0
..oo.4..oo.&#x  | 0 0 1 1 0 | * * * * * * 8 * * * * | 0 0 0 1 1 0 0
..... ...x.     | 0 0 0 2 0 | * * * * * * * 4 * * * | 0 0 0 1 0 1 0
...oo4...oo&#x  | 0 0 0 1 1 | * * * * * * * * 8 * * | 0 0 0 0 1 1 0
....x .....     | 0 0 0 0 2 | * * * * * * * * * 4 * | 0 0 0 0 1 0 1
..... ....x     | 0 0 0 0 2 | * * * * * * * * * * 4 | 0 0 0 0 0 1 1
----------------+-----------+-----------------------+--------------
x....4x....     | 8 0 0 0 0 | 4 4 0 0 0 0 0 0 0 0 0 | 1 * * * * * *
xux.. .....&#xt | 2 2 2 0 0 | 1 0 2 0 2 1 0 0 0 0 0 | * 4 * * * * *  {6}
..... xx...&#x  | 2 2 0 0 0 | 0 1 2 1 0 0 0 0 0 0 0 | * * 4 * * * *
..... .xwx.&#xt | 0 2 2 2 0 | 0 0 0 1 2 0 2 1 0 0 0 | * * * 4 * * *  {(h,H,H)2}
..xux .....&#xt | 0 0 2 2 2 | 0 0 0 0 0 1 2 0 2 1 0 | * * * * 4 * *  {6}
..... ...xx&#x  | 0 0 0 2 2 | 0 0 0 0 0 0 0 1 2 0 1 | * * * * * 4 *
....x4....x     | 0 0 0 0 8 | 0 0 0 0 0 0 0 0 0 4 4 | * * * * * * 1
or
o....4o....     & | 16  * * | 1 1  1 0  0 0 | 1 1 1 0  [4,6,8]
.o...4.o...     & |  * 16 * | 0 0  1 1  1 0 | 0 1 1 1  [4,6,H]
..o..4..o..       |  *  * 8 | 0 0  0 0  2 1 | 0 2 0 1  [h,6,6]
------------------+---------+---------------+--------
x.... .....     & |  2  0 0 | 8 *  * *  * * | 1 1 0 0
..... x....     & |  2  0 0 | * 8  * *  * * | 1 0 1 0
oo...4oo...&#x  & |  1  1 0 | * * 16 *  * * | 0 1 1 0
..... .x...     & |  0  2 0 | * *  * 8  * * | 0 0 1 1
.oo..4.oo..&#x  & |  0  1 1 | * *  * * 16 * | 0 1 0 1
..x.. .....       |  0  0 2 | * *  * *  * 4 | 0 2 0 0
------------------+---------+---------------+--------
x....4x....     & |  8  0 0 | 4 4  0 0  0 0 | 2 * * *
xux.. .....&#xt & |  2  2 2 | 1 0  2 0  2 1 | * 8 * *  {6}
..... xx...&#x  & |  2  2 0 | 0 1  2 1  0 0 | * * 8 *
..... .xwx.&#xt   |  0  4 2 | 0 0  0 2  4 0 | * * * 4  {(h,H,H)2}

Qqo xux4xxw&#zx   → heights = 0, where Q = 2q = 2.828427

o.. o..4o..     | 16  * * | 1 1  1 0  0 0 | 1 1 1 0  [4,6,8]
.o. .o.4.o.     |  * 16 * | 0 0  1 1  1 0 | 0 1 1 1  [4,6,H]
..o..4..o..     |  *  * 8 | 0 0  0 0  2 1 | 0 2 0 1  [h,6,6]
----------------+---------+---------------+--------
... x.. ...     |  2  0 0 | 8 *  * *  * * | 1 1 0 0
... ... x..     |  2  0 0 | * 8  * *  * * | 1 0 1 0
oo. oo.4oo.&#x  |  1  1 0 | * * 16 *  * * | 0 1 1 0
... ... .x.     |  0  2 0 | * *  * 8  * * | 0 0 1 1
.oo .oo4.oo&#x  |  0  1 1 | * *  * * 16 * | 0 1 0 1
... ..x ...     |  0  0 2 | * *  * *  * 4 | 0 2 0 0
----------------+---------+---------------+--------
... x..4x..     |  8  0 0 | 4 4  0 0  0 0 | 2 * * *
... xux ...&#xt |  2  2 2 | 1 0  2 0  2 1 | * 8 * *  {6}
... ... xx.&#x  |  2  2 0 | 0 1  2 1  0 0 | * * 8 *
.qo ... .xw&#zx |  0  4 2 | 0 0  0 2  4 0 | * * * 4  {(h,H,H)2}

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