Acronym	querco
TOCID symbol	rOC*
Name	quasirhombicuboctahedron, great rhombicuboctahedron (but not girco)
	© ©
Circumradius	sqrt[5-2 sqrt(2)]/2 = 0.736813
Inradius wrt. {3}	-[3-sqrt(2)]/sqrt(12) = -0.457777
Inradius wrt. {4}	(sqrt(2)-1)/2 = 0.207107
Coordinates	((sqrt(2)-1)/2, 1/2, 1/2)   & all permutations, all changes of sign
Vertex figure	[3/2,43]
Volume	[10 sqrt(2)-12]/3 = 0.392837
Surface	18+2 sqrt(3) = 21.464102
General of army	tic
Colonel of regiment	gocco
Dihedral angles	between {4} and {4}:   45° between {3} and {4}:   arccos(sqrt(2/3)) = 35.264390°
Face vector	24, 48, 26
Confer	compounds: rasquahpri   non-convex cap: rasquacu   general polytopal classes: Wythoffian polyhedra   analogs: quasirhombated hypercube qrbCn   quasiexpanded hypercube qeCn
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As abstract polytope querco is isomorphic to sirco, thereby replacing retrograde triangles by prograde ones. – As such querco is a lieutenant.

Just as sirco allows for a gyrated stack, esquigybcu (J37), this quasi-version too has an according gyrated stacking: rasquacu + inv stop + gyro rasquacu = gyquerco. In fact, both have the same vertex figure all over. But querco features full cubical symmetry, while gyquerco features 4-fold antiprismatic symmetry only, thereby dividing the according vertex set into 2 classes. As such gyquerco then would be the quasi-variant of esquigybcu.

This polyhedron is an edge-faceting of the great cubicuboctahedron (gocco).

Incidence matrix according to Dynkin symbol

x3/2o4x

.   . . | 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   . x |  4 |  2  2 | * 12 *
.   o4x |  4 |  0  4 | *  * 6

x4/3o3x

.   . . | 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   . x |  4 |  2  2 | * 12 *
.   o3x |  3 |  0  3 | *  * 8