The suborder Stephoidea, hitherto known by a few species only of "Acanthodesmida," comprises a large number of interesting Nassellaria (now more than two hundred species), which possess peculiar interest for the morphology and phylogeny of this legion. The monaxonian central capsule of the Stephoidea is surrounded either by one simple ring or by a complex system of several loosely connected rings; these may be united by a loose framework of connected branches, but never produce a complete lattice-shell, as is constantly the case in the Spyroidea, Botryodea, and Cyrtoidea. Therefore there remain between the parts of the connected rings a few large openings which we call "gates," separating them from the numerous small "pores" of the complete lattice-shells. In the most simple case, if only one ring be formed, there is also present only one "gate," the aperture of this simple ring.
The first known species of Stephoidea were observed in the Mediterranean by Johannes Müller in 1856, and described and figured in his last treatise (1858) under the names Lithocircus annularis (loc. cit., Taf. i. fig. 1) and Acanthodesmia vinculata (loc. cit., Taf. i. figs. 4-7). In the following year I myself observed two other living species in the Mediterranean, and described them in my Monograph (1862, pp. 268, 270) as Zygostephanus mülleri (Taf. xii. fig. 2) and Prismatium tripleurum (Taf. iv. fig. 6). For these four longest known Stephoidea I founded the new family of Acanthodesmida (loc. cit., p. 265), but united with them two other similar genera which I afterwards separated:—Plagiacantha (belonging to the Plectoidea) and Dictyocha (belonging to the Phæodaria).
When, in 1876, I received the rich material of the Challenger collection, I was astonished to find in it an enormous number of new, similar, and partly very interesting "Acanthodesmida," which were afterwards arranged in my Prodromus (1881, p. 444) in thirty-eight different genera and four "subfamilies," all united in one single large family, "Stephida or Monopylaria cricoidea." I retain here this natural group in the same sense, but give to it the rank of a "suborder," separating at the same time its four subfamilies as substantial "families." Since the names of the latter, proposed in the Prodromus, were not quite suitable, I replace them here by the following more convenient names:—
1. Family Stephanida (= Monostephida, 1881, p. 447). Skeleton entirely formed by one simple ring (the primary vertical sagittal ring). The only "gate" is the simple aperture of the ring.
2. Family Semantida (= Dyostephida, 1881, p. 446). Skeleton composed of two rings, perpendicular to one another; the primary vertical sagittal ring bears at the base a horizontal basal ring; between the two rings two or more "basal gates remain."
3. Family Coronida (= Triostephida, 1881, p. 445). Skeleton composed of two crossed vertical or meridional rings, perpendicular to one another—the primary sagittal ring and the secondary frontal ring. Commonly the two vertical rings are united at the base by a horizontal basal ring, and between them remain two or more "basal gates."
4. Family Tympanida (= Parastephida, 1881, p. 446). Skeleton composed of two parallel horizontal rings, and upper mitral ring, and a lower basal ring, both connected by vertical or divergent columellæ, which are parts of vertical rings (primary sagittal, and secondary frontal ring).
The peculiar structure of the central capsule of the Stephoidea, and their character as true Monopylea, were first recognised by Richard Hertwig, who in 1879, in his Organismus der Radiolarien, gave an excellent detailed description of it (loc. cit., pp. 68-72, Taf. vii. figs. 4, 5). He also pointed out the near affinity of these "Acanthodesmida" with the Spyroidea or Zygocyrtida, uniting the latter with the former family.
A fuller explanation of this affinity, and of the morphological and phylogenetic importance of the "Acanthodesmida," as ancestral forms of the Spyroidea and Cyrtoidea, was given in 1882 by Bütschli (Zeitschr. f. wiss. Zool., vol. xxxvi. pp. 495-501). He described in detail some important fossil forms of Acanthodesmida as different species of "Stephanolithis," a name which Ehrenberg had employed for various ring-like fragments of Radiolarian shells, sponges, and other fossil bodies. The four fossil species which Bütschli described represent four different genera of Stephoidea, viz., Semantis (spinescens), Semantrum (mülleri), Semantidium (haeckelii), and Tristephanium (hertwigii). On the phylogenetic conclusions, derived from these accurate observations, compare above, p. [893], &c. The topographical signification of the parts, employed by Bütschli, is contrary to mine; he calls my dorsal side the "anterior," and my ventral side the "posterior."
The geometrical fundamental form of the body in nearly all Stephoidea (with few exceptions) is distinctly bilateral or "dipleuric," so that we can easily distinguish the three different dimensive axes: the principal axis with different apical and basal poles, the sagittal axis with different dorsal and ventral poles, and the lateral axis with equivalent right and left poles. In only a few genera this bilateral symmetry is not expressed, and a simpler, more regular fundamental form appears. The latter may be either primary (in the monaxonian Archicircus and Lithocircus) or secondary, afterwards acquired (in the octahedral Trissocircus and Trissocyclus, the cubical Lithocubus, the prismatic Eutympanium, and some other forms).