The apophyses of the radial spines, by which the two concentric spherical shells are formed, seem to be constantly four on each spine, two being opposite in each shell. The proximal pair of opposite apophyses, forming the inner or medullary shell, is constantly much smaller than the distal pair composing the outer or cortical shell (Pl. [133], fig. 5). The proximal pair corresponds probably to the two primary apophyses of the Diporaspida (Phractaspis, Dorataspis, &c.), whilst the distal pair corresponds to the free apophyses of Orophaspis (Pl. [133], fig. 6). Therefore the Phractopeltida may be derived phylogenetically from the Diporaspida (not from the Tessaraspida). In the common ancestral genus of this family, Phractopelta, the free part of the radial spines (outside the outer shell) is quite simple, without free apophyses; in all other genera of the family that free part of the spines (either in all twenty spines or only in some of them) bears a third pair of lateral apophyses; these may be either simple or branched or even latticed; but the outer apophyses (of the third rank) remain constantly free, and a third lattice-shell is never formed by union of their edges (Pl. [133], figs. 2-4).

The inner lattice-shell of the Phractopeltida, or their "medullary shell," is constantly very small (commonly 0.03 to 0.05 mm. in diameter, rarely more). Its structure is difficult to make out; in the unbroken shell it is concealed by the dense network of the outer shell; in the broken shell it is commonly destroyed. Usually the pores of the inner shell are very small, circular or subcircular, scarcely as broad as the small separating bars. In the majority of Phractopeltida their number seems to be about forty, being probably the forty primary aspinal pores of the Diporaspida; in some species this number seems to be exceeded, so that perhaps some sutural pores may exist between the aspinal pores; but commonly the twenty plates composing the inner shell (each with two aspinal pores) seems to grow together perfectly by their meeting edges, so that there are no sutural pores between them. Evident sutures were not recognisable in the inner shell of any Phractopeltida.

The outer lattice-shell of the Phractopeltida, or their "cortical shell," is at least twice as broad, commonly about three times as broad, as the enclosed inner shell; it is much more varied in composition than the latter. Like the greater part of the Dorataspida we may distinguish here in the lattice-work two kinds of pores—parmal pores and sutural pores. The parmal pores are produced by the union of the meeting branches of the apophyses of each single spine, and are therefore visible on each isolated spine; whilst the sutural pores are formed by the meeting branches of the apophyses of neighbouring spines. The distinction of the parmal and the sutural pores, easy in most Dorataspida, is difficult in most Phractopeltida, because the sutures between the meeting branches are usually very early obliterated. However, the place of the obliterated suture is often indicated by the thickened condyles of the apophyses on both sides of the suture. Commonly also the form of the sutural pores is much more irregular than that of the parmal pores; the former are more or less constricted in the middle by the intumescence of the sutural condyles, whilst the latter are more roundish, elliptical, kidney-shaped, or square. The number of the pores in the outer shell in the typical normal form of Phractopeltida seems to be the same as in the most species of Dorataspis, Diporaspis, &c., between ninety and one hundred, viz., forty parmal pores and from fifty to sixty sutural pores. However, in many species this number is increased. Since in all Phractopeltida, each of the twenty plates is composed only of the meeting branches of two opposite apophyses, we find originally in each plate only two primary parmal pores or "aspinal pores." But in some species there occur four, six, or more pores in each plate; in this case two of them only are aspinal pores, all the others being "coronal pores." Moreover, in those species which exhibit on the base of each spine in the outer shell four crossed pores (Pl. [133], fig. 2), there are not four equivalent aspinal pores (as in the Tessaraspida), but the two opposite are primary or aspinal pores and the other two (different from them in size and form) coronal pores. However, the number of coronal pores in the Phractopeltida is never so large as in many Dorataspida, and the same holds good also for the increasing number of the irregular sutural pores. In none of the species observed does the total number of the pores in the outer shell reach two hundred.

The original mode of development of the apophyses composing the outer shell seems to be imitated by the free apophyses of the third order, which are developed from the radial spines outside the outer shell in all Phractopeltida, with the single exception of the simple ancestral genus Phractopelta. These apophyses of the third rank are also originally constantly two, opposite to one another (after the type of Lithophyllium, Dorataspis, &c.). Commonly they do not remain simple, but become branched, and by communication of the neighbouring branches small lattice-plates arise. Originally each of these free lattice-plates has only two parmal pores, but the number of the parmal pores increases afterwards, so that we may distinguish two (primary) aspinal pores, and two, four, or more (secondary) coronal pores. In the majority of species the two opposite apophyses are first crossed at right angles by a transverse beam, and the two parallel transverse beams are again crossed by perpendicular tertiary branches (again parallel to the apophyses). In this case the network of the free lattice-plates becomes more or less rectangular. But in other species the ramification of the apophyses assumes more the form of bifurcation or of irregular branching. As already said, the neighbouring free lattice-plates of this third order never meet, and therefore a complete third shell is never formed.

The different genera of Phractopeltida exhibit very remarkable differences in the development of free apophyses (or lattice-plates of the third order). Whilst in the numerous species of the ancestral genus Phractopelta all twenty spines remain simple, without such apophyses, only in a single observed species (representing the genus Pantopelta) were all twenty spines protected by them. In the three other genera only one part of the spines bears free apophyses, but not the other part. The most frequent form is Dorypelta (Pl. [133], fig. 2); here eight spines are simple (four equatorial and four polar spines of the hydrotomical plane), whilst twelve spines bear apophyses (eight tropical and four polar spines of the geotomical plane). In Octopelta the eight tropical spines only bear apophyses, whilst the twelve other (four equatorial and eight polar) are simple. In Stauropelta finally the four equatorial spines only are simple, whilst the sixteen other bear free apophyses (eight tropical and eight polar spines).

The Central Capsule of the Phractopeltida is constantly spherical, and enclosed between the two concentric spherical shells; it is therefore larger than the inner and smaller than the outer shell. Its wall is pierced by the twenty radial beams connecting the two shells. The shape of the central capsule and of the enveloping calymma is the same as in the other Acanthophracta and specially in the Dorataspida.

Synopsis of the Genera of Phractopeltida.
All twenty spines of the same form,All twenty spines without apophyses in the free external part,366. Phractopelta.
All twenty spines with apophyses in the free part,367. Pantopelta.
Twenty radial spines, partly without, partly with apophyses in the free external part,Eight tropical spines with apophyses, twelve others (eight polar and four equatorial) simple,368. Octopelta.
Twelve radial spines (eight tropical and four polar) with apophyses, eight others (four polar and four equatorial) simple,369. Dorypelta.
Sixteen radial spines (eight tropical and eight polar) with apophyses, four equatorial, simple,370. Stauropelta.
All twenty spines of the same form,
All twenty spines without apophyses in the free external part,
366. Phractopelta.
All twenty spines with apophyses in the free part,
367. Pantopelta.
Twenty radial spines, partly without, partly with apophyses in the free external part,
Eight tropical spines with apophyses, twelve others (eight polar and four equatorial) simple,
368. Octopelta.
Twelve radial spines (eight tropical and four polar) with apophyses, eight others (four polar and four equatorial) simple,
369. Dorypelta.
Sixteen radial spines (eight tropical and eight polar) with apophyses, four equatorial, simple,
370. Stauropelta.
Genus 366. Phractopelta,[[406]] Haeckel, 1881, Prodromus, p. 468.