If we take the latter, nearly identical form as the common starting point of both families of Cyclodiscaria, then probably Triopyle and Triolene must be regarded as retrograde forms, derived from Triodiscus in the one case, from Archidiscus in the other, by reduction of three interradial arm-chambers, whilst three perradial only remain. But it is also possible that the most simple form, Triolene, originated independently from some Cenosphæra, three simple radial chambers, like the latticed central chamber, being derived from the latter by apposition in three equidistant radii, whilst three other radii between them remained free. In this case the other genera of Pylodiscida are derived from their ancestral form Triolene.
Adopting this latter view, we find that all eight genera of Pylodiscida, here distinguished, may be regarded as following members of a continuous series. If the three simple arm-chambers of Triolene, surrounding the equal central chamber, become united at their distal ends by a concentric equatorial ring, then originates Triopyle; and this graduates into Triodiscus by fenestration of the three open gates between the three latticed arms. Whilst these three genera form together the subfamily Triopylida, a second family, Hexapylida, is composed of three other analogous genera, in which the same process of development becomes repeated.
Pylolena, the most simple form of Hexapylida, arises from Triodiscus by the development of three new arm-chambers (of the second order) which are apposed at the distal end of the three primary arm-chambers (of the first order) in the same radius. If the distal ends of these three secondary arm-chambers become united by a concentric latticed ring or girdle, we get Hexapyle (with six open gates, two in each radius), and if its six gates become afterwards closed by loose lattice-work, we arrive at Pylodiscus (a repetition of Triodiscus).
A third subfamily, Discopylida, is formed by the building of a chambered equatorial girdle around the margin of Pylodiscus. This girdle has quite the same structure as the similar chambered rings or girdles of the Porodiscida and Coccodiscida. Between the two sieve-plates of the disk surface is enclosed a variable number (twelve to twenty-four or more) of chambers, imperfectly separated by radial beams, which connect the margin of the Pylodiscus-shell with an outer peripheral concentric ring. In Discozonium this marginal ring is perfect, whilst in Discopyle it is interrupted by a peculiar large opening, a "marginal osculum" surrounded by a corona of spines, quite the same remarkable formation which we encountered in Ommatodiscus among the Porodiscida.
All Pylodiscida are therefore triradial (with three perradial arms and three interradial gates between them), and many of them have a great resemblance to certain triradial Porodiscida and Spongodiscida, perhaps not only a morphological resemblance, but also a true phylogenetic relation. But it is remarkable that we do not find further forms of development in this family, by multiplication either of the arm-chambers (further growth in the three perradii) or of the concentric chambered rings (in the periphery of the disk margin).
The central capsule of the Pylodiscida is constantly flat, discoidal, and enclosed between the two sieve-plates of the surface. Its form is either circular or triangular.
Synopsis of the Genera of the Pylodiscida.
I. Subfamily Triopylida. Three gates between three simple arm-chambers. |  | Three gates open, without a barring equatorial girdle, | 245. Triolena. | ||
| Three gates barred by a latticed equatorial girdle. |  | Gate-faces simple, | 246. Triopyle. | ||
| Gate-faces latticed, | 247. Triodiscus. | ||||
II. Subfamily Hexapylida. Six gates between three double arm-chambers (three inner and three outer); no chambered marginal girdle. | | Three outer gates open, without a barring equatorial girdle, | 248. Pylolena. | ||
| Three outer gates barred by a latticed (second) equatorial girdle. | | Both faces of the outer gates simple, | 249. Hexapyle. | ||
| Both faces of the outer gates latticed, | 250. Pylodiscus. | ||||
III. Subfamily Discopylida. Six gates between three double arm-chambers. | | In the equatorial plane on the margin of the Pylodiscus-shell is a chambered equatorial girdle. |  | No peculiar osculum on the margin of the disc, | 251. Discozonium. |
| One peculiar osculum (with a corona of spines) on the margin of the disc, | 252. Discopyle. | ||||
| I. Subfamily Triopylida. Three gates between three simple arm-chambers. | ||||||
| Three gates open, without a barring equatorial girdle, | ||||||
| 245. Triolena. | ||||||
| Three gates barred by a latticed equatorial girdle. | ||||||
| Gate-faces simple, | ||||||
| 246. Triopyle. | ||||||
| Gate-faces latticed, | ||||||
| 247. Triodiscus. | ||||||
| II. Subfamily Hexapylida. Six gates between three double arm-chambers (three inner and three outer); no chambered marginal girdle. | ||||||
| Three outer gates open, without a barring equatorial girdle, | ||||||
| 248. Pylolena. | ||||||
| Three outer gates barred by a latticed (second) equatorial girdle. | ||||||
| Both faces of the outer gates simple, | ||||||
| 249. Hexapyle. | ||||||
| Both faces of the outer gates latticed, | ||||||
| 250. Pylodiscus. | ||||||
| III. Subfamily Discopylida. Six gates between three double arm-chambers. | ||||||
| In the equatorial plane on the margin of the Pylodiscus-shell is a chambered equatorial girdle. | ||||||
| No peculiar osculum on the margin of the disc, | ||||||
| 251. Discozonium. | ||||||
| One peculiar osculum (with a corona of spines) on the margin of the disc, | ||||||
| 252. Discopyle. | ||||||