From Williams et al., 2017:

[Quinquecuspis, Harland, 1977b, p. 106-107;
Emendation: Harland, 1982, p. 396–397, as Protoperidinium subgenus Protoperidinium section Quinquecuspis (name not validly published).

Originally (and now) Quinquecuspis, subsequently Protoperidinium subgenus Protoperidinium section Quinquecuspis (name not validly published).
Tax. jr. syn.: Lejeunecysta, by implication in Matsuoka (1987, p.57), who incorrectly considered Lejeunecysta to be the senior name — however, this synonymy has not been generally followed. Harland (1982, p.396–397) considered Quinquecuspis Harland, 1977b to be not validly published, since it lacked a Latin diagnosis. As noted by Fensome et al. (1991, p.434), this was not necessary since the cysts are considered fossil and a Latin diagnosis is not required. Head (1993, p.31) contended that Quinquecuspis was not validly published in Harland (1977b) because as its type he designated a then unpublished species name, Trinovantedinium concretum Reid, 1977. Head believed that the paper by Reid (1977) was not published until 1978. However, although the journal in which Reid's paper appeared did indeed not come out until 1978, preprints of Reid's paper did appear in 1977 (P.C. Reid, personal communication, 1997). Accordingly Quinquecuspis was validly published in Harland (1977b).

Type species: originally as Trinovantedinium concretum, Reid, 1977 (pl.1, figs.9–11)] ; Quinquecuspis concreta, Harland, 1977

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Original description: [Harland, 1977]:

Diagnosis:
Pentagonal, peridinoid, acavate, brown cyst, made up of autophragm which thickens at the apex and antapex. Epitract conical or with shoulders, hypotract either carries symmetrical horns or is flat antapically.
Tabulation absent, cingulum conspicuous and planar, usually delimited by low ridges.
Sulcus very deeply indented and showing the reflected position of the flagellar pores.
Archeopyle basically intercalary formed by the loss of reflected plate ?2a but may also involve apical plate ?3`.

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Emended description as Protoperidinium subgenus Protoperidinium section Quinquecuspis:


Harland, 1982:

Diagnosis:
Pentagonal, peridinioid, acavate, brown cyst, made up of autophragm which thickens towards the apex and antapex. Epitract conical or with shoulders, hypotract with well or poorly developed asymmetrical horns.
Paratabulation absent, paracingulum conspicuous, planar, and delimited by low continuous or broken ridges. Deeply indented parasulcus sometimes with flagellar scars.
Archeopyle intercalary, standard hexa, formed by the loss of paraplate 2a, with or without an apical tongue. Operculum free.