Acronym girco
TOCID symbol tCO
Name great rhombicuboctahedron (but not querco),
truncated cuboctahedron
 
 © ©
Circumradius sqrt[13+6 sqrt(2)]/2 = 2.317611
Vertex figure [4,6,8]
Vertex layers
LayerSymmetrySubsymmetries
 o3o4oo3o .o . o. o4o
1x3x4xx3x .
{6} first
x . x
{4} first
. x4x
{8} first
2x3w .u . w. u4x
3u3w .x . X. x4w
4U3x .U . w. x4w
5ax3U .w . X. u4x
5bW . x
6aw3u .w . X. x4x
opposite {8}
6bW . x
7w3x .U . w 
8x3x .
opposite {6}
x . X
9 u . w
10x . x
opposite{4}
(X=x+q+q, W=u+w, U=x+w)
Lace city
in approx. ASCII-art
  x w  w x  
x   X  X   x
w X      X w
            
w X      X w
x   X  X   x
  x w  w x  
Coordinates ((1+2 sqrt(2))/2, (1+sqrt(2))/2, 1/2)   & all permutations, all changes of sign
General of army (is itself convex)
Colonel of regiment (is itself locally convex – no other uniform polyhedral members)
Dihedral angles
  • between {4} and {6}:   arccos(-sqrt(2/3)) = 144.735610°
  • between {4} and {8}:   135°
  • between {6} and {8}:   arccos(-1/sqrt(3)) = 125.264390°
Dual m3m4m
Confer
decompositions:
sirco || girco  
variations:
a3b4c   x3x4q   q3x4x   w3x4x  
general polytopal classes:
partial Stott expansions  
External
links
hedrondude   wikipedia   WikiChoron   mathworld   quickfur

As abstract polytope girco is isomorphic to quitco, thereby replacing octagons by octagrams.

Note that girco can be thought of as the external blend of 1 sirco + 8 tricues + 6 squacues + 12 cubes, cf. the Steward toroid K4 \ 8Q3(E4). This decomposition is also described as the degenerate segmentochoron xx3ox4xx&#xt.


Incidence matrix according to Dynkin symbol

x3x4x

. . . | 48 |  1  1  1 | 1  1 1
------+----+----------+-------
x . . |  2 | 24  *  * | 1  1 0
. x . |  2 |  * 24  * | 1  0 1
. . x |  2 |  *  * 24 | 0  1 1
------+----+----------+-------
x3x . |  6 |  3  3  0 | 8  * *
x . x |  4 |  2  0  2 | * 12 *
. x4x |  8 |  0  4  4 | *  * 6

snubbed forms: β3x4x, x3β4x, x3x4s, s3s4x, β3x4β, x3β4β, s3s4s, β3β4β

xxwwxx4xuxxux&#xt   → height(1,2) = height(2,3) = height(4,5) = height(5,6) = 1/sqrt(2) = 0.707107
                      height(3,4) = 1
({8} || pseudo (x,u)-{8} || pseudo (w,x)-{8} || pseudo (w,x)-{8} || pseudo (x,u)-{8} || {8})

o.....4o.....     | 8 * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 0
.o....4.o....     | * 8 * * * * | 0 0 1 1 1 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0 0
..o...4..o...     | * * 8 * * * | 0 0 0 0 1 1 1 0 0 0 0 0 0 | 0 0 1 1 1 0 0 0
...o..4...o..     | * * * 8 * * | 0 0 0 0 0 0 1 1 1 0 0 0 0 | 0 0 0 1 1 1 0 0
....o.4....o.     | * * * * 8 * | 0 0 0 0 0 0 0 0 1 1 1 0 0 | 0 0 0 1 0 1 1 0
.....o4.....o     | * * * * * 8 | 0 0 0 0 0 0 0 0 0 0 1 1 1 | 0 0 0 0 0 1 1 1
------------------+-------------+---------------------------+----------------
x..... ......     | 2 0 0 0 0 0 | 4 * * * * * * * * * * * * | 1 1 0 0 0 0 0 0
...... x.....     | 2 0 0 0 0 0 | * 4 * * * * * * * * * * * | 1 0 1 0 0 0 0 0
oo....4oo....&#x  | 1 1 0 0 0 0 | * * 8 * * * * * * * * * * | 0 1 1 0 0 0 0 0
.x.... ......     | 0 2 0 0 0 0 | * * * 4 * * * * * * * * * | 0 1 0 1 0 0 0 0
.oo...4.oo...&#x  | 0 1 1 0 0 0 | * * * * 8 * * * * * * * * | 0 0 1 1 0 0 0 0
...... ..x...     | 0 0 2 0 0 0 | * * * * * 4 * * * * * * * | 0 0 1 0 1 0 0 0
..oo..4..oo..&#x  | 0 0 1 1 0 0 | * * * * * * 8 * * * * * * | 0 0 0 1 1 0 0 0
...... ...x..     | 0 0 0 2 0 0 | * * * * * * * 4 * * * * * | 0 0 0 0 1 1 0 0
...oo.4...oo.&#x  | 0 0 0 1 1 0 | * * * * * * * * 8 * * * * | 0 0 0 1 0 1 0 0
....x. ......     | 0 0 0 0 2 0 | * * * * * * * * * 4 * * * | 0 0 0 1 0 0 1 0
....oo4....oo&#x  | 0 0 0 0 1 1 | * * * * * * * * * * 8 * * | 0 0 0 0 0 1 1 0
.....x ......     | 0 0 0 0 0 2 | * * * * * * * * * * * 4 * | 0 0 0 0 0 0 1 1
...... .....x     | 0 0 0 0 0 2 | * * * * * * * * * * * * 4 | 0 0 0 0 0 1 0 1
------------------+-------------+---------------------------+----------------
x.....4x.....     | 8 0 0 0 0 0 | 4 4 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * *
xx.... ......&#x  | 2 2 0 0 0 0 | 1 0 2 1 0 0 0 0 0 0 0 0 0 | * 4 * * * * * *
...... xux...&#xt | 2 2 2 0 0 0 | 0 1 2 0 2 1 0 0 0 0 0 0 0 | * * 4 * * * * *
.xwwx. ......&#xt | 0 2 2 2 2 0 | 0 0 0 1 2 0 2 0 2 1 0 0 0 | * * * 4 * * * *
...... ..xx..&#x  | 0 0 2 2 0 0 | 0 0 0 0 0 1 2 1 0 0 0 0 0 | * * * * 4 * * *
...... ...xux&#xt | 0 0 0 2 2 2 | 0 0 0 0 0 0 0 1 2 0 2 0 1 | * * * * * 4 * *
....xx ......&#x  | 0 0 0 0 2 2 | 0 0 0 0 0 0 0 0 0 1 2 1 0 | * * * * * * 4 *
.....x4.....x     | 0 0 0 0 0 8 | 0 0 0 0 0 0 0 0 0 0 0 4 4 | * * * * * * * 1
or
o.....4o.....      & | 16  *  * | 1 1  1 0  0 0 0 | 1 1 1 0 0
.o....4.o....      & |  * 16  * | 0 0  1 1  1 0 0 | 0 1 1 1 0
..o...4..o...      & |  *  * 16 | 0 0  0 0  1 1 1 | 0 0 1 1 1
---------------------+----------+-----------------+----------
x..... ......      & |  2  0  0 | 8 *  * *  * * * | 1 1 0 0 0
...... x.....      & |  2  0  0 | * 8  * *  * * * | 1 0 1 0 0
oo....4oo....&#x   & |  1  1  0 | * * 16 *  * * * | 0 1 1 0 0
.x.... ......      & |  0  2  0 | * *  * 8  * * * | 0 1 0 1 0
.oo...4.oo...&#x   & |  0  1  1 | * *  * * 16 * * | 0 0 1 1 0
...... ..x...      & |  0  0  2 | * *  * *  * 8 * | 0 0 1 0 1
..oo..4..oo..&#x     |  0  0  2 | * *  * *  * * 8 | 0 0 0 1 1
---------------------+----------+-----------------+----------
x.....4x.....      & |  8  0  0 | 4 4  0 0  0 0 0 | 2 * * * *
xx.... ......&#x   & |  2  2  0 | 1 0  2 1  0 0 0 | * 8 * * *
...... xux...&#xt  & |  2  2  2 | 0 1  2 0  2 1 0 | * * 8 * *
.xwwx. ......&#xt    |  0  4  4 | 0 0  0 2  4 0 2 | * * * 4 *
...... ..xx..&#x     |  0  0  4 | 0 0  0 0  0 2 2 | * * * * 4

wx3xx3xw&#zx   → height = 0
(tegum sum of 2 mutually inverse (w,x,x)-toes)

o.3o.3o.     | 24  * |  1  1  1  0  0 | 1 1  1 0
.o3.o3.o     |  * 24 |  0  0  1  1  1 | 0 1  1 1
-------------+-------+----------------+---------
.. x. ..     |  2  0 | 12  *  *  *  * | 1 0  1 0
.. .. x.     |  2  0 |  * 12  *  *  * | 1 1  0 0
oo3oo3oo&#x  |  1  1 |  *  * 24  *  * | 0 1  1 0
.x .. ..     |  0  2 |  *  *  * 12  * | 0 1  0 1
.. .x ..     |  0  2 |  *  *  *  * 12 | 0 0  1 1
-------------+-------+----------------+---------
.. x.3x.     |  6  0 |  3  3  0  0  0 | 4 *  * *
wx .. xw&#zx |  4  4 |  0  2  4  2  0 | * 6  * *
.. xx ..&#x  |  2  2 |  1  0  2  0  1 | * * 12 *
.x3.x ..     |  0  6 |  0  0  0  3  3 | * *  * 4
or
o.3o.3o.     & | 48 |  1  1  1 | 1 1  1
---------------+----+----------+-------
.. x. ..     & |  2 | 24  *  * | 1 0  1
.. .. x.     & |  2 |  * 24  * | 1 1  0
oo3oo3oo&#x    |  2 |  *  * 24 | 0 1  1
---------------+----+----------+-------
.. x.3x.     & |  6 |  3  3  0 | 8 *  *
wx .. xw&#zx   |  8 |  0  4  4 | * 6  *
.. xx ..&#x    |  4 |  2  0  2 | * * 12

xwX wxx4xux&#zxt   → height = 0, X=x+q+q = 3.828427

o.. o..4o..     | 16  *  * | 1 1  1 0  0 0 0 | 1 1 1 0 0
.o. .o.4.o.     |  * 16  * | 0 0  1 1  1 0 0 | 0 1 1 1 0
..o ..o4..o     |  *  * 16 | 0 0  0 0  1 1 1 | 0 0 1 1 1
----------------+----------+-----------------+----------
x.. ... ...     |  2  0  0 | 8 *  * *  * * * | 1 1 0 0 0
... ... x..     |  2  0  0 | * 8  * *  * * * | 1 0 1 0 0
oo. oo.4oo.&#x  |  1  1  0 | * * 16 *  * * * | 0 1 1 0 0
... .x. ...     |  0  2  0 | * *  * 8  * * * | 0 1 0 1 0
.oo .oo4.oo&#x  |  0  1  1 | * *  * * 16 * * | 0 0 1 1 0
... ..x ...     |  0  0  2 | * *  * *  * 8 * | 0 0 0 1 1
... ... ..x     |  0  0  2 | * *  * *  * * 8 | 0 0 1 0 1
----------------+----------+-----------------+----------
x.. ... x..     |  4  0  0 | 2 2  0 0  0 0 0 | 4 * * * *
xw. wx. ...&#zx |  4  4  0 | 2 0  4 2  0 0 0 | * 4 * * *
... ... xux&#xt |  2  2  2 | 0 1  2 0  2 0 1 | * * 8 * *
... .xx ...&#x  |  0  2  2 | 0 0  0 1  2 1 0 | * * * 8 *
... ..x4..x     |  0  0  8 | 0 0  0 0  0 4 4 | * * * * 2

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