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There are several families of symmetric polytopes with irreducible symmetry which have a member in more than one dimensionality. These are tabulated here with Petrie polygon projection graphs and Coxeter–Dynkin diagrams.
Table of irreducible polytope families  

Family n  nsimplex  nhypercube  northoplex  ndemicube  1_{k2}  2_{k1}  k_{21}  pentagonal polytope  
Group  A_{n}  B_{n} 

 H_{n}  
2    pgon (example: p=7)  Hexagon  Pentagon  
3  Tetrahedron  Cube  Octahedron  Tetrahedron  Dodecahedron  Icosahedron  
4  5cell   16cell   24cell  120cell  600cell  
5  5simplex  5cube  5orthoplex  5demicube  
6  6simplex  6cube  6orthoplex  6demicube  1_{22}  2_{21}  
7  7simplex  7cube  7orthoplex  7demicube  1_{32}  2_{31}  3_{21}  
8  8simplex  8cube  8orthoplex  8demicube  1_{42}  2_{41}  4_{21}  
9  9simplex  9cube  9orthoplex  9demicube  
10  10simplex  10cube  10orthoplex  10demicube 