form p | q r, and it is regular if q=2 or q=r. The Coxeter-Dynkin diagram is another symbolic representation that shows the quasiregular relation between the two dual-regular forms: The convex quasiregular polyhedra There are two uniform convex quasiregular polyhedra: The cuboctahedron , vertex configuration (3.4)2, Coxeter-Dynkin diagram The icosidodecahedron , vertex configuration (3.5)2, Coxeter-Dynkin diagram In addition, the octahedron, which is also regular, , vertex configuration (3.3)2, can be considered quasiregular if alternate faces are given different colors. In this form it is sometimes known as the tetratetrahedron. The remaining convex regular polyhedra have an odd number of faces at each vertex so cannot be colored in a way that preserves edge transitivity. It has Coxeter-Dynkin diagram Each of these forms the common core of a dual pair of regular polyhedra. The names of two of these give clues to the associated dual pair: respectively cube octahedron, and icosahedron dodecahedron. The octahedron is the common core of a dual pair of tetrahedra (a compound known as the stella octangula); when derived in this way, the octahedron is sometimes called the tetratetrahedron, as tetrahedron tetrahedron. Each of these quasiregular polyhedra can be constructed by a rectification operation on either regular parent, truncating the vertices fully, until each original edge is reduced to its midpoint. Quasiregular tilings This sequence continues as the trihexagonal tiling, vertex figure (3.6)2 - a quasiregular tiling based on the triangular tiling and hexagonal tiling. The checkerboard pattern is a quasiregular coloring of the square tiling, vertex figure (4.4)2: The triangular tiling can also be considered quasiregular, with three sets of alternating triangles at each vertex, (3.3)3: In the hyperbolic plane, this sequence continues further, for example the triheptagonal tiling, vertex figure (3.7)2 - a quasiregular tiling based on the order-7 triangular tiling and heptagonal tiling. Nonconvex examples Coxeter, H.S.M. et al. (1954) also classify certain star polyhedra, having the same characteristics, as being quasiregular. Two are based on dual pairs of regular Kepler–Poinsot solids, in the same way as for the convex examples: the great icosidodecahedron , and the dodecadodecahedron : Nine more are the hemipolyhedra, which are faceted forms of the aforementioned quasiregular polyhedra derived from rectification of regular polyhedra. These include equatorial faces passing through the centre of the polyhedra: Lastly there are three ditrigonal forms, all facetings of the regular dodecahedron, whose vertex figures contain three alternations of the two face types: