the four equatorial spines are of equal dimensions (Icosacantha). (See Gener. Morphol., Bd. i. p. 436-446.)
34. The Amphithect Dipyramidal or Lentelliptical Ground-Forms.—The ground-forms whose geometrical type is the lenticular or "triaxial" ellipsoid, may also be designated amphithect double pyramids; they are characterised by the possession of a vertical main axis which has similar poles, and is crossed at its middle by two transverse axes, unequal but isopolar. The horizontal equatorial plane of the body is therefore an amphithect or elongated polygon (a rhombus in the simplest case possible), and divides the whole body into two equal amphithect pyramids. The simplest and commonest form of this group is the rhombic octahedron, which is also the ground-form of the rhombic crystallographic system. It plays an important part in those Acantharia in which twenty radial spines are disposed according to the Müllerian Law, but in which the two pairs of equatorial spines are unequal (different geotomical and hydrotomical axes, see p. 719); to this category belong the Amphilonchida (Pl. 132), Belonaspida (Pl. 136), Hexalaspida (Pl. 139), and Diploconida (Pl. 140). A form essentially identical obtains also among the Spumellaria in the majority of the Larcoidea, both in their triaxial lattice-shells, and in their lentelliptical central capsules, which present geometrically accurate triaxial ellipsoids, with three unequal isopolar axes at right angles to each other. (See Gener. Morphol., Bd. i. p. 446-452.)
35. The Regular Pyramidal Ground-Forms.—The ground-forms whose geometrical type is the regular pyramid, and which are the most conspicuous in the Medusæ, Polyps, Corals, and regular Echinoderms (the Radiata of earlier authors), are almost confined among the Radiolaria to the legion Nassellaria; they occur, however, in the great majority of these, and especially in those families which may be classed together as "Cyrtoidea triradiata et multiradiata." Strictly speaking, however, almost all these Nassellaria, at all events in their origin, are bilateral or dipleuric, since the primary sagittal ring with its characteristic apophyses marks out the sagittal median plane, and further, since the three feet of the basal tripod are usually divided into an unpaired dorsal (pes caudalis) and two paired ventral or lateral (pedes pectorales, dexter et sinister). On the other hand, it is noteworthy, firstly, that among the primitive Plectoidea there are perfectly regular radial forms, without any indication of an original bilateral symmetry, and secondly, that similar forms are also very common among the Cyrtoidea, probably as secondary radial forms, developed from primitive bilateral ones. Similar cases also occur in certain Phæodaria (e.g., the Medusettida and Tuscarorida, Pls. 100, 120), but they are entirely wanting among the Acantharia and Spumellaria. The multiradial Nassellaria have arisen from the triradial by the interpolation of three, six, nine, or more interradial and adradial secondary apophyses between the three primary perradial ones. (See Gener. Morphol., Bd. i. pp. 459-874.)
