The apex was a cap worn by the flamines

Flamen

In ancient Roman religion, a flamen was a priest assigned to one of fifteen deities with official cults during the Roman Republic. The most important three were the flamines maiores , who served the three chief Roman gods of the Archaic Triad. The remaining twelve were the flamines minores...

 and Salii at Rome

Rome

Rome is the capital of Italy and the country's largest and most populated city and comune, with over 2.7 million residents in . The city is located in the central-western portion of the Italian Peninsula, on the Tiber River within the Lazio region of Italy.Rome's history spans two and a half...

. The essential part of the apex, to which alone the name properly belonged, was a pointed piece of olive-wood, the base of which was surrounded with a lock of wool. This was worn on the top of the head, and was held there either by fillets only, or, as was more commonly the case, was also fastened by means of two strings or bands, which were called apicula (Festus

Festus

Festus is a Latin word meaning "festive, festal, joyful, merry" and may refer to:* Festus, Missouri, a town in the United States*Festus, a poem by the English poet Philip James Bailey*Drew Hankinson, professional wrestler...

, s.v.), or offendices (Festus, s.v.), though the latter word is also interpreted to mean a kind of button, by which the strings were fastened under the chin (cf. Serv. ad Virg. Aen. ii.683, viii.664, x.270).

The flamines were forbidden by law to go into public, or even into the open air without the apex (Gellius x.15), and hence we find the expression of alicui apicem dialem imponere used as equivalent to the appointment of a Flamen Dialis

Flamen Dialis

In ancient Roman religion, the Flamen Dialis was the high priest of Jupiter. There were 15 flamines, of which three were flamines maiores, serving the three gods of the Archaic Triad...

(Livy

Livy

Titus Livius — known as Livy in English — was a Roman historian who wrote a monumental history of Rome and the Roman people. Ab Urbe Condita Libri, "Chapters from the Foundation of the City," covering the period from the earliest legends of Rome well before the traditional foundation in 753 BC...

 vi.41). Sulpicius was deprived of the priesthood, only because the apex fell from his head whilst he was sacrificing (Valerius Maximus

Valerius Maximus

Valerius Maximus was a Latin writer and author of a collection of historical anecdotes. He worked during the reign of Tiberius .-Biography:...

 i.1 §5).

Dionysius of Halicarnassus

Dionysius of Halicarnassus

Dionysius of Halicarnassus was a Greek historian and teacher of rhetoric, who flourished during the reign of Caesar Augustus. His literary style was Attistic — imitating Classical Attic Greek in its prime.-Life:...

 (ii.70) describes the cap as being of a conical form. On ancient monuments we see it round as well as conical.

The Albogalerus, or albus galerus was a white cap worn by the flamen dialis, made of the skin of a white victim sacrificed to Jupiter, and had the apex fastened to it by means of an olive-twig (Festus, s.v. albogalerus; Gell. x.15).

From apex was formed the epithet apicatus, applied to the flamen dialis by Ovid

Ovid

Publius Ovidius Naso , known as Ovid in the English-speaking world, was a Roman poet who is best known as the author of the three major collections of erotic poetry: Heroides, Amores, and Ars Amatoria...

(Fast. iii.197).