Acronym co   (alt.: rotet)
TOCID symbol CO, rTT
Name cuboctahedron,
rhombitetratetrahedron,
rectified cube,
rectified octahedron,
cantellated tetrahedron,
trigonal gyrobicupola

` © ©`
Vertex figure [(3,4)2] = x q
Snub derivation
Vertex layers
 Layer Symmetry Subsymmetries o3o4o o3o . o . o . o4o 1 o3x4o o3x .{3} first o . overtex first . x4o{4} first 2 x3x . x . qvertex figure . o4q 3 x3o .opposite {3} u . o . x4oopposite {4} 4 x . q 5 o . oopposite vertex o3o3o o3o . o . o . o3o 1 x3o3x x3o .{3} first x . x{4} first . o3x{3} first 2a x3x . q . o . x3x 2b o . q 3 o3x .opposite {3} x . xopposite {4} . x3oopposite {3}
Lace city
in approx. ASCII-art
```  x  o
x  u  x
o  x
```
```o q o
q   q
o q o
```
Coordinates (1/sqrt(2), 1/sqrt(2), 0)   & all permutations, all changes of sign
General of army (is itself convex)
Colonel of regiment (is itself locally convex – other uniform polyhedral members: cho   oho – other edge facetings)
Confer
Grünbaumian relatives:
2co   2co+16{3}
related Johnson solids:
tricu   tobcu   etigybcu
variations:
a3b3c   q3o3x   f3o3x   v3o3x   u3o3x
compounds:
arie
External

Incidence matrix according to Dynkin symbol

```o3x4o

. . . | 12 |  4 | 2 2
------+----+----+----
. x . |  2 | 24 | 1 1
------+----+----+----
o3x . |  3 |  3 | 8 *
. x4o |  4 |  4 | * 6
```

```o3/2x4o

.   . . | 12 |  4 | 2 2
--------+----+----+----
.   x . |  2 | 24 | 1 1
--------+----+----+----
o3/2x . |  3 |  3 | 8 *
.   x4o |  4 |  4 | * 6
```

```o4/3x3o

.   . . | 12 |  4 | 2 2
--------+----+----+----
.   x . |  2 | 24 | 1 1
--------+----+----+----
o4/3x . |  4 |  4 | 6 *
.   x3o |  3 |  3 | * 8
```

```o4/3x3/2o

.   .   . | 12 |  4 | 2 2
----------+----+----+----
.   x   . |  2 | 24 | 1 1
----------+----+----+----
o4/3x   . |  4 |  4 | 6 *
.   x3/2o |  3 |  3 | * 8
```

```x3o3x

. . . | 12 |  2  2 | 1 2 1
------+----+-------+------
x . . |  2 | 12  * | 1 1 0
. . x |  2 |  * 12 | 0 1 1
------+----+-------+------
x3o . |  3 |  3  0 | 4 * *
x . x |  4 |  2  2 | * 6 *
. o3x |  3 |  0  3 | * * 4
```

```x3/2o3/2x

.   .   . | 12 |  2  2 | 1 2 1
----------+----+-------+------
x   .   . |  2 | 12  * | 1 1 0
.   .   x |  2 |  * 12 | 0 1 1
----------+----+-------+------
x3/2o   . |  3 |  3  0 | 4 * *
x   .   x |  4 |  2  2 | * 6 *
.   o3/2x |  3 |  0  3 | * * 4
```

```s4x3o

demi( . . . ) | 12 |  2  2 | 2 1 1
--------------+----+-------+------
demi( . x . ) |  2 | 12  * | 1 1 0
sefa( s4x . ) |  2 |  * 12 | 1 0 1
--------------+----+-------+------
s4x .   ♦  4 |  2  2 | 6 * *
demi( . x3o ) |  3 |  3  0 | * 4 *
sefa( s4x3o ) |  3 |  0  3 | * * 4
```

```xxo3oxx&#xt   → both heights = sqrt(2/3) = 0.816497
({3} || pseudo {6} || dual {3})

o..3o..    | 3 * * | 2 2 0 0 0 0 | 1 2 1 0 0 0
.o.3.o.    | * 6 * | 0 1 1 1 1 0 | 0 1 1 1 1 0
..o3..o    | * * 3 | 0 0 0 0 2 2 | 0 0 0 1 2 1
-----------+-------+-------------+------------
x.. ...    | 2 0 0 | 3 * * * * * | 1 1 0 0 0 0
oo.3oo.&#x | 1 1 0 | * 6 * * * * | 0 1 1 0 0 0
.x. ...    | 0 2 0 | * * 3 * * * | 0 1 0 1 0 0
... .x.    | 0 2 0 | * * * 3 * * | 0 0 1 0 1 0
.oo3.oo&#x | 0 1 1 | * * * * 6 * | 0 0 0 1 1 0
... ..x    | 0 0 2 | * * * * * 3 | 0 0 0 0 1 1
-----------+-------+-------------+------------
x..3o..    | 3 0 0 | 3 0 0 0 0 0 | 1 * * * * *
xx. ...&#x | 2 2 0 | 1 2 1 0 0 0 | * 3 * * * *
... ox.&#x | 1 2 0 | 0 2 0 1 0 0 | * * 3 * * *
.xo ...&#x | 0 2 1 | 0 0 1 0 2 0 | * * * 3 * *
... .xx&#x | 0 2 2 | 0 0 0 1 2 1 | * * * * 3 *
..o3..x    | 0 0 3 | 0 0 0 0 0 3 | * * * * * 1

or
o..3o..    & | 6 * | 2  2 0 | 1 2 1
.o.3.o.      | * 6 | 0  2 2 | 0 2 2
-------------+-----+--------+------
x.. ...    & | 2 0 | 6  * * | 1 1 0
oo.3oo.&#x & | 1 1 | * 12 * | 0 1 1
.x. ...    & | 0 2 | *  * 6 | 0 1 1
-------------+-----+--------+------
x..3o..    & | 3 0 | 3  0 0 | 2 * *
xx. ...&#x & | 2 2 | 1  2 1 | * 6 *
.xo ...&#x & | 1 2 | 0  2 1 | * * 6
```

```xox4oqo&#xt   → both heights = 1/sqrt(2) = 0.707107
({4} || dual pseudo q-{4} || {4})

o..4o..     | 4 * * | 2 2 0 0 | 1 2 1 0 0
.o.4.o.     | * 4 * | 0 2 2 0 | 0 1 2 1 0
..o4..o     | * * 4 | 0 0 2 2 | 0 0 1 2 1
------------+-------+---------+----------
x.. ...     | 2 0 0 | 4 * * * | 1 1 0 0 0
oo.4oo.&#x  | 1 1 0 | * 8 * * | 0 1 1 0 0
.oo4.oo&#x  | 0 1 1 | * * 8 * | 0 0 1 1 0
..x ...     | 0 0 2 | * * * 4 | 0 0 0 1 1
------------+-------+---------+----------
x..4o..     | 4 0 0 | 4 0 0 0 | 1 * * * *
xo. ...&#x  | 2 1 0 | 1 2 0 0 | * 4 * * *
... oqo&#xt | 1 2 1 | 0 2 2 0 | * * 4 * *
.ox ...&#x  | 0 1 2 | 0 0 2 1 | * * * 4 *
..x4..o     | 0 0 4 | 0 0 0 4 | * * * * 1

or
o..4o..     & | 8 * | 2  2 | 1 2 1
.o.4.o.       | * 4 | 0  4 | 0 2 2
--------------+-----+------+------
x.. ...     & | 2 0 | 8  * | 1 1 0
oo.4oo.&#x  & | 1 1 | * 16 | 0 1 1
--------------+-----+------+------
x..4o..     & | 4 0 | 4  0 | 2 * *
xo. ...&#x  & | 2 1 | 1  2 | * 8 *
... oqo&#xt   | 2 2 | 0  4 | * * 4
```

```oxuxo oqoqo&#xt   → all heights = 1/2
(pt || pseudo (x,q)-{4} || pseudo line || pseudo (x,q)-{4} || pt)

o.... o....     | 1 * * * * | 4 0 0 0 0 0 0 | 2 2 0 0 0 0
.o... .o...     | * 4 * * * | 1 1 1 1 0 0 0 | 1 1 1 1 0 0
..o.. ..o..     | * * 2 * * | 0 0 2 0 2 0 0 | 0 1 2 0 1 0
...o. ...o.     | * * * 4 * | 0 0 0 1 1 1 1 | 0 0 1 1 1 1
....o ....o     | * * * * 1 | 0 0 0 0 0 0 4 | 0 0 0 0 2 2
----------------+-----------+---------------+------------
oo... oo...&#x  | 1 1 0 0 0 | 4 * * * * * * | 1 1 0 0 0 0
.x... .....     | 0 2 0 0 0 | * 2 * * * * * | 1 0 0 1 0 0
.oo.. .oo..&#x  | 0 1 1 0 0 | * * 4 * * * * | 0 1 1 0 0 0
.o.o. .o.o.&#x  | 0 1 0 1 0 | * * * 4 * * * | 0 0 1 1 0 0
..oo. ..oo.&#x  | 0 0 1 1 0 | * * * * 4 * * | 0 0 1 0 1 0
...x. .....     | 0 0 0 2 0 | * * * * * 2 * | 0 0 0 1 0 1
...oo ...oo&#x  | 0 0 0 1 1 | * * * * * * 4 | 0 0 0 0 1 1
----------------+-----------+---------------+------------
ox... .....&#x  | 1 2 0 0 0 | 2 1 0 0 0 0 0 | 2 * * * * *
..... oqo..&#xt | 1 2 1 0 0 | 2 0 2 0 0 0 0 | * 2 * * * *
.ooo. .ooo.&#xt | 0 1 1 1 0 | 0 0 1 1 1 0 0 | * * 4 * * *
.x.x. .....&#x  | 0 2 0 2 0 | 0 1 0 2 0 1 0 | * * * 2 * *
..... ..oqo&#xt | 0 0 1 2 1 | 0 0 0 0 2 0 2 | * * * * 2 *
...xo .....&#x  | 0 0 0 2 1 | 0 0 0 0 0 1 2 | * * * * * 2

or
o.... o....      & | 2 * * | 4 0 0 0 | 2 2 0 0
.o... .o...      & | * 8 * | 1 1 1 1 | 1 1 1 1
..o.. ..o..        | * * 2 | 0 0 4 0 | 0 2 2 0
-------------------+-------+---------+--------
oo... oo...&#x   & | 1 1 0 | 8 * * * | 1 1 0 0
.x... .....      & | 0 2 0 | * 4 * * | 1 0 0 1
.oo.. .oo..&#x   & | 0 1 1 | * * 8 * | 0 1 1 0
.o.o. .o.o.&#x     | 0 2 0 | * * * 4 | 0 0 1 1
-------------------+-------+---------+--------
ox... .....&#x   & | 1 2 0 | 2 1 0 0 | 4 * * *
..... oqo..&#xt  & | 1 2 1 | 2 0 2 0 | * 4 * *
.ooo. .ooo.&#xt    | 0 2 1 | 0 0 2 1 | * * 4 *
.x.x. .....&#x     | 0 4 0 | 0 2 0 2 | * * * 2
```