Another kind of triradial structure characterises the genera Plagiacantha and Plectophora. The three radial spines united in the central point lie here not in one plane, but diverge in different planes, so that they correspond to the three lateral edges of a three-sided pyramid. Commonly the three spines are of equal size, and also the angles between them equal, so that the pyramid is regular, sometimes very flat, at other times more elevated. Spicula of exactly the same form are also found in some Beloidea. Probably the three divergent spines are homologous to the three basal feet of numerous Spyroidea and Cyrtoidea. The central capsule, according to Hertwig, is placed in the apical part of the pyramid, the axes of both being identical, and the porochora resting in the apex itself. This fact seems to contradict the above-mentioned affinity; but since in Triplecta and Triplagia the three spines lie horizontally, they may have changed this original position in different direction, in Plagiacantha and Plectophora becoming divergent upwards, whereas in Plagoniscus and Plectaniscus (as in the Spyroidea and Cyrtoidea) directed downwards.
The triradial structure, common to the Triplagida and Triplectida, is replaced by the quadriradial structure in the Tetraplagida and Tetraplectida. Probably the latter have been derived from the former by development of a fourth spine, and then this latter would correspond to the "apical horn" of the other Nassellaria. But possibly also both structures have originated independently from one another. We may distinguish not less than four different kinds of the quadriradial structure. In the first case all four spines are equal, and diverge from a common central point at equal angles in different directions, corresponding to the four axes of a regular tetrahedron (Tetraplagia and Tetraplecta, Pl. [91], figs. 3, 8).
In the second case all four spines are also equal, but they are not united in a common central point, but opposite in pairs on the two poles of a common central rod (Plagonidium). Therefore the skeleton possesses here the same form as in the "geminate-biradiate" spicula of many Beloidea (e.g., Thalassoxanthium bifurcum and Sphærozoum furcatum). The development of the short horizontal middle rod, connecting the two divergent pairs of spines, is here probably effected by the porochora of the central capsule resting upon it.
Whilst in these two cases of quadriradial structure all four spines are equal, in two other cases they become differentiated in a very remarkable manner. One spine is vertically directed upwards, in shape and size different from the three others, which are directed downwards; the former corresponding probably to the "apical horn," the latter to the three "basal feet," which are found in the great majority of the Spyroidea and Cyrtoidea. Therefore we encounter here for the first time that characteristic "cortinar structure" which is complete in Cortina and Cortiniscus (Pl. [92], figs. 11-13, 21), and which may be regarded as the strongest argument for a close relationship, or even for a common monophyletic origin of all Nassellaria.
The four spines, which we regard therefore as "cortinar spines," exhibit a twofold kind of central junction. In the simpler case they are united in a common central point, on which rests the porochora of the central capsule (Plagoniscus and Plectaniscus, Pl. [91], figs. 4, 9). These forms are nearer to Cortina, and may be derived immediately from Tetraplagia and Tetraplecta by differentiation of the four equal spines. In the other case the four cortinar spines are separated in pairs, diverging from the two poles of a short horizontal common "central rod" (Plagiocarpa and Periplecta, Pl. [91], figs. 5, 10). These forms may be compared with the spicula of some Beloidea and derived from Plagonidium; but their basal central rod may be compared again with the basal part of the sagittal ring of Cortina, and this comparison becomes very important in those forms like Plagiocarpa procortina (Pl. [91], fig. 5). Here the four spines approach very nearly to those of Cortina; the two ventral spines (or pectoral feet) on the anterior pole of of the middle rod are equal, but very different from the two dorsal spines, arising from the posterior pole; the lower odd spine of the latter corresponds to the "caudal foot," the upper spine to the "apical horn" of Cortina and of the Cyrtellaria. The vertical plane, determined by these two dorsal spines, is the sagittal plane, and two opposite curved branches which lie in this plane (an upper arising from the basal part of the apical spine and a lower arising from the anterior pole of the middle rod) may be regarded as ventral parts of an incomplete sagittal ring. This interesting form and some other similar Tetraplagida may be regarded either as beginning Stephoidea (Cortina, with incomplete sagittal ring) or as retrograde Stephoidea (Cortina, with partly reduced sagittal ring). In every case they seem to indicate the near relationship between the Stephoidea and Plectoidea.
Another argument for this close relationship may be found in the position of the central capsule in the interesting genus Plagiocarpa (Pl. [91], fig. 5). Its basal part (with the porochora) rests upon the common central rod, its ventral face upon the ventral prolongation of the latter, its dorsal face upon the apical horn; its axis lies in the sagittal plane. The three basal spines (the odd caudal and the paired pectoral feet) diverge from its basal pole downwards in the same manner as in the Cortina, the Zygospyrida and the Monocyrtida.
Less important than those quadriradial Tetraplagida and Tetraplectida, are the sexradial Plectoidea, the Hexaplagida and Hexaplectida. These may be derived immediately from the triradial Plectoidea by prolongation of the three primary original spines (of Plagiacantha) over the common central point. Here also two different kinds of central junction are found. In the simpler case all six radial spines arise from a common central point (Hexaplagia and Hexaplecta). In the other case the six radial spines arise from the two poles of a short horizontal common central rod, opposed in two groups, each of three spines (Plagonium and Plectanium, Pl. [91], figs. 6, 11). In this latter case the single corresponding spines of the two opposite groups are usually parallel, and exhibit therefore exactly the same characteristic "germinate-triradiate" form which is found in many Beloidea (e.g., in the common Sphærozoum punctatum and the similar Lampoxanthium punctatum).
The fourth and last group of this suborder contains the multiradiate Plectoidea, the Polyplagida and Polyplectida. Here the number of radial spines, diverging from the common centre, exceeds six, and is commonly seven to nine, at other times ten to twelve or more (Polyplagia and Polyplecta, Pl. [91], fig. 12). When these two genera are better known from further accurate observations, they may probably be divided into several different genera (as already proposed in my Prodromus, 1881), since not only the number, but also the central junction and the arrangement of the numerous radial spines in the few observed species seems to be very different. In some seven-radiate species (e.g., Polyplecta heptacantha) four larger spines seem to be true "cortinar spines," the three smaller secondary productions of the former. In the nine-radiate species the nine spines seem to be sometimes basal branches of three primary spines, at other times six secondary intercalated between the three primary (like Enneaphormis, Pl. [57], fig. 9). In those multiradial Plectoidea, in which the number of spines amounts to ten or twelve or more, the laws of disposition are not yet recognised.
Comparing these different productions of the skeleton in the numerous Plectoidea, we find expressed two remarkable and very different affinities. On the one hand many Plectoidea exhibit exactly the same peculiar forms, which are only found besides in the Beloidea (as many species of Triplagia, Plagiacantha, Tetraplagia, Plagonidium, Hexaplagia, and Plagonium). On the other hand many Plectoidea bear the same characteristic composition of the skeleton (or the "cortinar structure") which is found in the Cortinida among the Stephoidea, and in numerous Spyroidea and Cyrtoidea, which all agree in the possession of three divergent basal feet and a vertical apical horn. A most important argument for the close affinity of all these "cortinar Nassellaria" seems to be given by the fact that the sagittal ring, which in Cortina is combined with the quadriradial structure, exhibits in the Cyrtellaria the most different stages of development; in one group it is complete, in the second incomplete, and in the third it has completely disappeared.
The form of the radial spines composing the skeleton is usually three-sided prismatic, gradually tapering from the thicker central base towards the distal apex; sometimes they are slender pyramidal. More rarely the spines are cylindrical or slender conical. In the majority of species the spines are straight, in the minority more or less curved. In very few species only are they quite simple, without branches. They are nearly always more or less branched, in many larger species very richly ramified. The modes of ramification are rather variable. In the majority of Plectoidea the spines are rather regularly verticillate, bearing an increasing number of verticils, each of which is composed of three divergent branches. These arise from the three edges of the spine, and all the branches of one edge are usually parallel, either perpendicular to the spine, or directed at an acute angle towards its apex. When the verticils are numerous (five to ten or more), their size commonly tapers gradually towards the apex. Pinnate spines occur more rarely than verticillate ones; in this case the two paired lateral edges only of the prismatic spine bear opposite or alternate branches, whilst the odd middle edge bears no ramules. In some species the spines are singly or doubly forked. In many species (mainly those with cylindrical spines) the ramification of the spines is more or less irregular.