23. _The Subsidiary Groups of Geometrical Ground-Forms._--The four natural principal groups of ground-forms, which have just been defined according to the nature of the centre of their bodies, may be divided again into numerous subsidiary groups, defined by the relations of the constant axes and the two poles of each axis, as well as by the number of the axes and the differentiation of the secondary with respect to the principal axis. The most important of these subsidiary groups into which the principal ones are immediately divided are the following:--(1) The _Centrostigma_ (or sphærotypic) are divided into spheres (Homaxonia) and endospherical polyhedra (Polyaxonia). (2) The _Centraxonia_ (or grammotypic) into uniaxial (Monaxonia) and those with crossed axes (Stauraxonia); among the former of these may be distinguished the isopolar (phacotypic) and the allopolar (conotypic); among the latter the double and single pyramids. (3) The _Centroplana_ (or bilaterals) are divided into amphipleura (or bilaterally radial) and zygopleura (or bilaterally symmetrical). (4) The _Acentrica_ (or Anaxonia) or absolutely irregular ground-forms, present no special subdivisions. For a complete system of the geometrical ground-forms and their relation to promorphological classification, see Gener. Morphol., Bd. i. pp. 555-558. 24. _The Spherical or Homaxon Ground-Form._--The spherical is the only absolutely regular ground-form, since only in it are all axes which pass through the centre equal; it is very often realised among the Radiolaria, especially in the SPUMELLARIA and ACANTHARIA, where it furnishes the common original ground-form, but it is often to be seen in the shells of many PHÆODARIA (in most #Phæosphæria#); on the other hand, it is never found among the NASSELLARIA. Geometrical spheres, in the strict sense of the term, are only to be found among the SPUMELLARIA and ACANTHARIA, namely, in the central capsule of many #Collodaria# (Pls. 1, 2) and all #Sphæroidea# (Pls. 11-30) as well as many Acanthometra and Acanthophracta (Pls. 128-138). Nevertheless, speaking generally, one includes those central capsules and skeletons which have been distinguished here as endospherical polyhedra. (On these ground-forms see Gener. Morphol., Bd. i. pp. 404-406.)