a vertical Schläfli symbol , and Coxeter diagram . The snub cuboctahedron is the alternation of the truncated cuboctahedron, , and . Regular polyhedra with even-order vertices can also be snubbed as alternated truncations, like the snub octahedron, as , , is the alternation of the truncated octahedron, , and . The snub octahedron represents the pseudoicosahedron, a regular icosahedron with pyritohedral symmetry. The snub tetratetrahedron, as , and , is the alternation of the truncated tetrahedral symmetry form, , and . Coxeter's snub operation also allows n-antiprisms to be defined as or , based on n-prisms or , while 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: Examples Nonuniform snub polyhedra Nonuniform polyhedra with all even-valance vertices can be snubbed, including some infinite sets; for example: Coxeter's uniform snub star-polyhedra Snub star-polyhedra are constructed by their Schwarz triangle (p q r), with rational ordered mirror-angles, and all mirrors active and alternated. Coxeter's higher-dimensional snubbed polytopes and honeycombs In general, a regular polychoron with Schläfli symbol , and Coxeter diagram , has a snub with extended Schläfli symbol , and . A rectified polychoron = r{p,q,r}, and has snub symbol = sr{p,q,r}, and . Examples There is only one uniform convex snub in 4-dimensions, the snub 24-cell. The regular 24-cell has Schläfli symbol, , and Coxeter diagram , and the snub 24-cell is represented by , Coxeter diagram . It also has an index 6 lower symmetry constructions as or s{31,1,1} and , and an index 3 subsymmetry as or sr{3,3,4}, and or . The related snub 24-cell honeycomb can be seen as a or s{3,4,3,3}, and , and lower symmetry or sr{3,3,4,3} and or , and lowest symmetry form as or s{31,1,1,1} and . A Euclidean honeycomb is an alternated hexagonal slab honeycomb, s{2,6,3}, and or sr{2,3,6}, and or sr{2,3[3]}, and . Another Euclidean (scaliform) honeycomb is an alternated square slab honeycomb, s{2,4,4}, and or sr{2,41,1} and : The only uniform snub hyperbolic uniform honeycomb is the snub hexagonal tiling honeycomb, as s{3,6,3} and , which can also be constructed as an alternated hexagonal tiling honeycomb, h{6,3,3}, . It is also constructed as s{3[3,3]} and . Another hyperbolic (scaliform) honeycomb is a snub order-4 octahedral honeycomb, s{3,4,4}, and . See also Snub polyhedron References Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973),