This construction requires "q" to be even. A quasiregular polyhedron formula_4 or "r"{"p","q"}, with Coxeter diagram or has a quasiregular truncation defined as formula_5 or "tr"{"p","q"}, and Coxeter diagram or and quasiregular snub defined as an alternated truncated rectification formula_6 or "htr"{"p","q"} = "sr"{"p","q"}, and Coxeter diagram or . For example, Kepler's snub cube is derived from the quasiregular cuboctahedron, with a vertical Schläfli symbol formula_7, and Coxeter diagram , and so is more explicitly called a snub cuboctahedron, expressed by a vertical Schläfli symbol formula_8 and Coxeter diagram . The snub cuboctahedron is the alternation of the "truncated cuboctahedron", formula_9 and . Regular polyhedra with even-order vertices to also be snubbed as alternated truncation, like a "snub octahedron", formula_10, (and "snub tetratetrahedron", as formula_11, ) represents the pseudoicosahedron, a regular icosahedron with pyritohedral symmetry. The "snub octahedron" is the alternation of the truncated octahedron, formula_12 and , or tetrahedral symmetry form: formula_13 and . Coxeter's snub operation also allows n-antiprisms to be defined as formula_14 or formula_15, based on n-prisms formula_16 or formula_17, while formula_18 is a regular n-hosohedron, a degenerate polyhedron, but a valid tiling on the sphere with digon or lune-shaped faces. The same process applies for snub tilings:  Nonuniform polyhedra with all even-valance vertices can be snubbed, including some infinite sets, for example:  Snub star-polyhedra are constructed by their Schwarz triangle (p q r), with rational ordered mirror-angles, and all mirrors active and alternated. In general, a regular polychoron with Schläfli symbol, formula_19, and Coxeter diagram , has a snub with extended Schläfli symbol formula_20, and .