From Fensome et al., 2019:
Peridictyocysta mirabilis (Cookson and Eisenack, 1958, p.48, pl.8, figs.3–5) Cookson and Eisenack, 1974, p.70. Holotype: Cookson and Eisenack, 1958, pl.8, fig.3. Originally Cannosphaeropsis, subsequently (and now) Peridictyocysta. Age: Late Jurassic.

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Locus typicus: Omati, Papua
Stratum typicum: Late Jurassic

Original description: Cookson and Eisenack, 1958, p. 48: Cannosphaeropsis mirabilis
Shell elongate-oval, membrane thin, firm, smooth with 4-6 approximately longitudinal rows of evenly-spaced, solid processes which are connected with one another both proximally and distally by short threads to form a rather smallmeshed superficial network. Short spine-like outgrowth are sometimes present on the connecting threads. In the holotype, a pylome appears to be present at one end of the shell.

Dimensions: Type - 90 x 62 µm overall; shell - 62 x 35 µm; range - 90-109 x 57-71 µm overall; shell 62-85 x 28-52 µm.

Affinities:
Cookson and Eisenack, 1958, p. 48: Cannosphaeropsis mirabilis
C. mirabilis is distinct from all known species of Cannosphaeropsis in the elongated form of the shell.