# Quasirhombicuboctahedron

(Redirected from Querco)
Quasirhombicuboctahedron Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymQuerco
Coxeter diagramx4/3o3x (       )
Elements
Faces8 triangles, 6+12 squares
Edges24+24
Vertices24
Vertex figureCrossed isosceles trapezoid, edge lengths 1, 2, 2, 2 Measures (edge length 1)
Circumradius$\frac{\sqrt{5-2\sqrt2}}{2} \approx 0.73681$ Volume$2\frac{5\sqrt2-6}{3} \approx 0.71404$ Dihedral angles4–4: 45°
4–3: $\arccos\left(\frac{\sqrt6}{3}\right) \approx 35.26439^\circ$ Central density5
Number of external pieces488
Level of complexity73
Related polytopes
ArmyTic, edge length $\sqrt2-1$ RegimentGocco
DualGreat deltoidal icositetrahedron
ConjugateSmall rhombicuboctahedron
Convex coreChamfered cube
Abstract & topological properties
Flag count192
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryB3, order 48
ConvexNo
NatureTame

The quasirhombicuboctahedron, also commonly known as the nonconvex great rhombicuboctahedron, or querco is a uniform polyhedron. It consists of 8 triangles and 6+12 squares, with one triangle and three squares meeting at each vertex. It also has 6 octagrammic pseudofaces. It can be obtained by quasicantellation of the cube or octahedron, or equivalently by pushing either polyhedron's faces inward and filling the gaps with squares.

6 of the squares in this figure have full BC2 symmetry, while 12 of them have only A1×A1 symmetry with respect to the whole polyhedron.

It is also sometimes called a great rhombicuboctahedron, but is not to be confused with the convex polyhedron with the same name.

It is a faceting of the great cubicuboctahedron, using the original's squares and triangles, while also introducing 12 additional squares.

## Related polyhedra

The rhombisnub quasirhombicosicosahedron is a uniform polyhedron compound composed of 5 quasirhombicuboctahedra.

The quasirhombicuboctahedron can be constructed as an octagrammic prism augmented with retrograde square cupolas facing inwards on the octagrammic faces.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the great cubicuboctahedron.

o4/3o3o truncations
Name OBSA Schläfli symbol CD diagram Picture
Cube cube {4/3,3} x4/3o3o (       )
Quasitruncated hexahedron quith t{4/3,3} x4/3x3o (       )
Cuboctahedron co r{3,4/3} o4/3x3o (       )
Truncated octahedron toe t{3,4/3} o4/3x3x (       )
Octahedron oct {3,4/3} o4/3o3x (       )
Quasirhombicuboctahedron querco rr{3,4/3} x4/3o3x (       )
Quasitruncated cuboctahedron quitco tr{3,4/3} x4/3x3x (       )
(degenerate, oct+6(4)) o4/3o3ß (       )
Icosahedron ike s{3,4/3} o4/3s3s (       )