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	Layer Symmetry Subsymmetries   o3o4o o3o . o . o . o4o 1 x3x4x x3x . {6} first x . x {4} first . x4x {8} first 2 x3w . u . w . u4x 3 u3w . x . Q . x4w 4 X3x . X . w . x4w 5a x3X . w . Q . u4x 5b W . x 6a w3u . w . Q . x4x opposite {8} 6b W . x 7 w3x . X . w   8 x3x . opposite {6} x . Q 9   u . w 10 x . x opposite{4} (Q=x+q+q, W=u+w, X=x+w)
Lace city in approx. ASCII-art	x w w x x Q Q x w Q Q w w Q Q w x Q Q 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)
Confer	variations: a3b4c   x3x4q   q3x4x   w3x4x
External links

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

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

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