Acronym	socco
TOCID symbol	bCO
Name	small cubicuboctahedron
VRML	⭳ ©
Circumradius	sqrt[5+2 sqrt(2)]/2 = 1.398966
Inradius wrt. {3}	-[3+sqrt(2)]/sqrt(12) = -1.274274
Inradius wrt. {4}	(1+sqrt(2))/2 = 1.207107
Inradius wrt. {8}	1/2 = 0.5
Vertex figure	[3/2,8,4,8]
Snub derivation / VRML	⭳
Coordinates	((1+sqrt(2))/2, 1/2, 1/2)   & all permutations, all changes of sign
Volume	[6+8 sqrt(2)]/3 = 5.771236
Surface	18+12 sqrt(2)+2 sqrt(3) = 38.434664
General of army	sirco
Colonel of regiment	sirco
Dihedral angles	between {4} and {8}:   90° between {3} and {8}:   arccos[1/sqrt(3)] = 54.735610°
Face vector	24, 48, 20
Confer	compounds: rahrie   general polytopal classes: Wythoffian polyhedra   analogs: socco series
External links

As abstract polytope socco is isomorphic to gocco, thereby replacing octagons by octagrams. – As such socco is a lieutenant.

The small cubicuboctahedron is an edge-faceting of the small rhombicuboctahedron (sirco).

Incidence matrix according to Dynkin symbol

    x    
 4 / \ 4 
  x---o  
   3/2   

x3/2o4x4*a

.   . .    | 24 |  2  2 | 1 2 1
-----------+----+-------+------
x   . .    |  2 | 24  * | 1 1 0
.   . x    |  2 |  * 24 | 0 1 1
-----------+----+-------+------
x3/2o .    |  3 |  3  0 | 8 * *
x   . x4*a |  8 |  4  4 | * 6 *
.   o4x    |  4 |  0  4 | * * 6

    x     
 4 / \ 4/3
  x---o   
    3     

x4/3o3x4*a

.   . .    | 24 |  2  2 | 1 2 1
-----------+----+-------+------
x   . .    |  2 | 24  * | 1 1 0
.   . x    |  2 |  * 24 | 0 1 1
-----------+----+-------+------
x4/3o .    |  4 |  4  0 | 6 * *
x   . x4*a |  8 |  4  4 | * 6 *
.   o3x    |  3 |  0  3 | * * 8

β3o4x

both( . . . ) | 24 |  2  2 | 1 1 2
--------------+----+-------+------
both( . . x ) |  2 | 24  * | 0 1 1
sefa( β3o . ) |  2 |  * 24 | 1 0 1
--------------+----+-------+------
      β3o .   ♦  3 |  0  3 | 8 * *
both( . o4x ) |  4 |  4  0 | * 6 *
sefa( β3o4x ) |  8 |  4  4 | * * 6

starting figure: x3o4x