☆ Space-filling convex polyhedra: the triangular prism, hexagonal prism, cube, truncated octahedron, and gyrobifastigium. While the cube is the only Platonic solid that can tessellate space on its own, the truncated octahedron and the gyrobifastigium are the only Archimedean and Johnson solids, respectively,  that can also tessellate space with their own copies. ☆ Cell-transitive parallelohedra: any parallelepiped, as well as the rhombic dodecahedron and elongated dodecahedron, and the hexagonal prism and truncated octahedron. The cube is a special case of a parallelepiped, with the rhombic dodecahedron the only Catalan solid to tessellate space on its own. ☆ Regular abstract polyhedra, which include the excavated dodecahedron and the dodecadodecahedron. They have combinatorial symmetries transitive on flags of their elements, with topologies equivalent to that of toroids and the ability to tile the hyperbolic plane.
Of precisely five different conjugacy classes of maximal subgroups of 
  
    
      
        
          
            M
          
          
            11
          
        
      
    
    {\displaystyle \mathrm {M} _{11}}
  , one is the almost simple symmetric group 
  
    
      
        
          
            S
          
          
            5
          
        
      
    
    {\displaystyle \mathrm {S} _{5}}
   (of order 5!