Phylum Radiolaria Müller, 1858 see Subphylum Radiozoa Cavalier-Smith, 1987
   Superclass Polycystina Ehrenberg, 1838 see Superclass Polycystinia Ehrenberg, 1838
     Class Nassellaria Ehrenberg, 1847
       Order Spyridinata Ehrenberg, 1847
         Family Acanthodesmiidae Haeckel, 1862
           Subfamily Acanthodesmiinae Haeckel, 1862
             01 Genus Acanthodesmia Müller, 1856
             02 Genus Acrocubus Haeckel, 1881
             03 Genus †Dipocoronis Haeckel, 1881
             04 Genus Eucoronis Haeckel, 1881
             05 Genus Semantis Haeckel, 1887
             06 Genus Tetracubus Haeckel, 1887
             07 Genus Tricyclidium Haeckel, 1881
             08 Genus †Tripocubus Haeckel, 1887
             09 Genus Trissocyclus Haeckel, 1881
             10 Genus Trissocyrcus Nazarov, 1975, nom. null. see Genus Trissocircus Haeckel, 1881
             11 Genus Tympanidium Haeckel, 1881
             12 Genus Tympaniscus Haeckel, 1887
             13 Genus †Tympanomma Haeckel, 1887
             14 Genus Zygostephanus Haeckel, 1862