Quasirhombicuboctahedron
Quasirhombicuboctahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Space | Spherical |
Notation | |
Bowers style acronym | Querco |
Coxeter diagram | x4/3o3x () |
Elements | |
Faces | 8 triangles, 6+12 squares |
Edges | 24+24 |
Vertices | 24 |
Vertex figure | Crossed isosceles trapezoid, edge lengths 1, √2, √2, √2 |
Measures (edge length 1) | |
Circumradius | |
Volume | |
Dihedral angles | 4–4: 45° |
4–3: | |
Central density | 5 |
Number of external pieces | 488 |
Level of complexity | 73 |
Related polytopes | |
Army | Tic, edge length |
Regiment | Gocco |
Dual | Great deltoidal icositetrahedron |
Conjugate | Small rhombicuboctahedron |
Convex core | Chamfered cube |
Abstract & topological properties | |
Flag count | 192 |
Euler characteristic | 2 |
Orientable | Yes |
Genus | 0 |
Properties | |
Symmetry | B_{3}, order 48 |
Convex | No |
Nature | Tame |
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 BC_{2} symmetry, while 12 of them have only A_{1}×A_{1} 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[edit | edit source]
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[edit | edit source]
Its vertices are the same as those of its regiment colonel, the great cubicuboctahedron.
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 () |
External links[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#46).
- Klitzing, Richard. "querco".
- Wikipedia Contributors. "Nonconvex great rhombicuboctahedron".
- McCooey, David. "Uniform Great Rhombicuboctahedron"