From Fensome et al., 2019:

Tetrachacysta Backhouse, 1988, p.109–110.
Type: Backhouse, 1988, pl.42, figs.1a–b; text-figs.32B–C, as Tetrachacysta allenii.

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Original description: [Backhouse, 1988]:

Synopsis:
Cysts small, quadrilobate with a waisted paracingular zone. Surface features low, usually evenly distributed; paratabulation not indicated, or poorly expressed by surface features. Archeopyle apical, type (tA).

Description:
Shape: Quadrilobate, rounded subquadrangular in outline.
Wall relationships: Autophragm only.
Wall features: Generally no parasutural features. Surface features low, usually evenly distributed and regular in size, or slightly larger on the extremities of the cyst.
Paratabulation: Generally indicated only by the archeopyle and the archeopyle suture which indicates 6 precingular paraplates.
Paratabulation may be poorly expressed by surface features.
Archeopyle: Apical, type (tA), operculum free.
Paracingulum: Generally not expressed- cyst constricted in the paracingular zone.
Parasulcus: Not expressed.
Size: Small.