27. _The Regular Dodecahedral Ground-Form._--The ground-form whose geometrical type is the regular dodecahedron (or pentagonal dodecahedron), bounded by twelve equilateral and equiangular pentagons, is very rarely found perfectly developed, as in _Circorrhegma dodecahedra_ (Pl. 117, fig. 2). This form is by no means so common among the Radiolaria as in the pollen grains of plants (_e.g._, _Buchholzia maritima_, _Fumaria spicata_, _Polygonum amphibium_, &c.). It can, however, be regarded as present in all those #Sphæroidea# whose spherical lattice-shells bear twenty equal and equidistant radial spines (_e.g._, many species of _Acanthosphæra_, _Heliosphæra_, and other Astrosphærida); the basal points of these spines mark out the twenty angles of the regular pentagonal dodecahedron. (See Gener. Morphol., Bd. i. p. 412.) 28. _The Regular Octahedral Ground-Form._--The ground-form whose geometrical type is the regular octahedron (bounded by eight equilateral triangles), commonly appears among the SPUMELLARIA in the family Cubosphærida (p. 169, Pls. 21-25). In {xiv}these #Sphæroidea# the typical ground-form is usually indicated by six equal radial spines, which are opposed to each other in pairs, and lie in three similar axes perpendicular to each other; these are the three axes of the tesseral crystallographic system; one of them is vertical, whilst the other two cross each other at right angles in its centre. Occasionally, too, the spherical form of the lattice-shell passes over into that of the regular octahedron (Pl. 22, figs. 8, 10). The same form recurs in _Circoporus_ (Pl. 117, fig. 6) among the PHÆODARIA. In the vegetable kingdom it is exhibited by the antheridia of _Chara_. It is not found in the NASSELLARIA and ACANTHARIA. (See Gener. Morphol., Bd. i. p. 412.) 29. _The Regular Cubic Ground-Form._--The ground-form whose geometrical type is that of a die or cube, is actually presented in a very striking manner by various Radiolaria. Among the SPUMELLARIA it occurs in certain #Sphæroidea#, _e.g._, in the Astrosphærid genera _Centrocubus_ and _Octodendron_ (Pl. 18, figs. 1-3); in these the central medullary shell is a complete cube, bounded by six equal squares, from the eight angles of which eight equal radial spines project. This form can also be regarded as present in those #Sphæroidea# whose spherical lattice-shell bears eight equal and equidistant radial spines (many Astrosphærida). Besides these the cubic ground-form is to be seen in certain NASSELLARIA of the family Tympanida, especially in _Lithocubus_ (Pl. 82, fig. 12; Pl. 94, fig. 13), in many species of _Acrocubus_, _Microcubus_, &c.; the twelve bars of its lattice-skeleton correspond often exactly to the edges of the cube. (See Gener. Morphol., Bd. i. p. 413.)