[Class] Polycystinea Ehrenberg, 1838 - polycystines see Superclass Polycystinia Ehrenberg, 1838
   Order Nassellaria Ehrenberg, 1875 see Class Nassellaria Ehrenberg, 1847
     Family Trissocyclidae Haeckel, 1881 see Family Acanthodesmiidae Haeckel, 1862
       01 Genus Acanthodesmia Müller, 1856
       02 Genus †Acrocubus Haeckel, 1881
       03 Genus †Acrospyris Haeckel, 1881
       04 Genus †Amphispyris Haeckel, 1881
       05 Genus Androspyris Haeckel, 1887
       06 Genus Cantharospyris Haeckel, 1887
       07 Genus Cephalospyris Haeckel, 1881
       08 Genus Ceratospyris Ehrenberg, 1847
       09 Genus †Clathrospyris Haeckel, 1881
       10 Genus Corythospyris Haeckel, 1881
       11 Genus Dendrospyris Haeckel, 1881
       12 Genus †Desmospyris Haeckel, 1881
       13 Genus †Dictyospyris Ehrenberg, 1847
       14 Genus †Dorcadospyris Haeckel, 1881
       15 Genus †Eucoronis Haeckel, 1881
       16 Genus †Giraffospyris Haeckel, 1881
       17 Genus †Gorgospyris Haeckel, 1881
       18 Genus †Lamprospyris Haeckel, 1881
       19 Genus Liriospyris Haeckel, 1881
       20 Genus †Lithocircus Müller, 1856
       21 Genus †Lithotympanum Haeckel, 1881
       22 Genus Lophospyris Haeckel, 1881
       23 Genus Nephrospyris Haeckel, 1887 see Genus Nephrodictyum Haeckel, 1881
       24 Genus Paradictyum Haeckel, 1881
       25 Genus †Petalospyris Ehrenberg, 1847
       26 Genus Phormospyris Haeckel, 1881
       27 Genus Platybursa Haeckel, 1881
       28 Genus †Psychospyris Riedel & Sanfilippo, 1971
       29 Genus †Rhodospyris Haeckel, 1881
       30 Genus Semantis Haeckel, 1887
       31 Genus Tholospyris Haeckel, 1881
       32 Genus Triceraspyris Haeckel, 1881
       33 Genus †Tricolospyris Haeckel, 1881
       34 Genus †Tristylospyris Haeckel, 1881
       35 Genus †Tympanidium Haeckel, 1881
       36 Genus †Tympanomma Haeckel, 1887
       37 Genus Zygocircus Bütschli, 1881
       38 Genus †Zygospyris Haeckel, 1887