I just wanted to share some information I've gathered regarding Eikas:
“The birthday of Epicurus continued to be kept regularly as an annual festival by his followers; and the monthly meetings on the 20th (Eikas) became so prominent a feature of the sect in the eyes of the world, that the Epicureans came to be nicknamed Eikadistæ (or Men of the Twentieth.) Pictures of Epicurus were found in the rooms and bedchambers of Epicureans, and even on their rings and their plates.” (William Wallace, Epicureanism)
“On the twentieth day of every month his followers assmbled to perform solemn rites in honor of his memory, a sort of sacrament. […] The twentieth was also sacred to Apollo, which gave it an additional sanctity. Such notoriety eventually attached itself to these monthly memorial gatherings that Epicureans were dubbed “Twentyers” by was of derision. […] Fairly early in the years of his residence in Athens, if not from the outset, certain nights were set apart for a sort of philosophical symposium, where special formalities were observed. We may assume that it was open to adult members only. On these occasions the customery austerity of diet was abandoned, and the wine and viands, if we can trust the testimony of adversaries, were of the best. […] As for the intellectual fare of these ritualistic banquets […] the renegade Timocrates […] dubbed them Euphranta, “Feasts of Reason,” as it were. […] Especially enlightening is the knowledge that these gatherings were appointed for the twentieth of each month. If after the death of Epicurus they were to be perpetuated in emmory of himself and Metrodorus, why not on the anniversary of his birth […] The answer is that the twentieth in the Greek calendar was invested with something of the sanctity of a sabbath. It had a name of its own, eikas, like the Ides in the Roman calendar. It was a sacred day in the cult of Apollo and it was on the twentieth that the final rites of the initiation were performend in the mysteries of Demeter. It follows that once in every year, at the same time that the secrets of the afterlife were bieing revealed by the hierophant at Eleusis, the disciples in the house in Melite were celebrating what Metrodorus styled ‘the divine orgies’’ of Epicurus. Thus the master himself was a hierophant; he actually spoke of his own pronouncements as oracles, and Lucretius ranked them higher than those of the Pythian priestess. […] Because of the custom the Epicureans were dubbed eikadistae, “Twentyers,” as already mentioned. […] the private letters […] were especially adapted to keep alive in the hearts and minds of the disciples the memory of those who had gone before. They constituted a suppporting literature that reinforced the effect of the monthly gatherings everywhere celebrated on the twentieth to commemorate the memory of the founders. […] the plain diet of the school was replaced on the twentieth of each month by more bountiful repasts. These celebrations marked the high points of the fellowship for which the sect was notorious.” (De Witt, Epicurus and His Philosophy 3; 52; 104-105; 120)
“[B]oth he and Metrodorus received honours on the twentieth day of each month. A yearly cult to the dead is a familiar practice in Greece. A monthly cult was reserved for divinities: Artemis had a cult on the sixth day of a month and Apollo on the seventh. Apollo, the god sacred to Socrates and Plato, also had a cult on the twentieth of the month. The Epicureans came to be known as Members of the Cult of the Twentieth (Eikadistai). We learn from an inscription from Athens of a group organized around the cult of the hero Eikadeus in the worship of Apollo Pernessios […] The Epicurean cult of the twentieth was, therefore, conceived of as a cult to Epicurus and Metrodorus as divinities. Their votaries were known as eikadistai. ” (The Cambridge Guide to Epicureanism 23-24)
“Commemorative Epicurean gatherings in honor of Epicurus and Metrodorus emulated Athenian religious worship of Apollo by honoring the hero Eikadeus on twentieth of each month.” (Daniel Marković, “The Rhetoric of Explanation in Lucretius’ De rerum natura”)
“As an example of these [pre-Epicurean] clubs or conspiracies for mutual support […] we may cite the association called oi Eikadeis […] These Eikadeis are an association, the members of which are bound to each other by a common oath, as well as by a curse which the mythical hero of the association, Eikadeus, is supposed to have imprecated” (George Grote, A HIstory of Greece, Volume 8, 17)
“The emblematic activity of the Epicureans was the feast on the twentieth of every Greek month, earning them the nickname eikadistae, ‘Twentyers.’ From a partly obliterated atext from a later Epicurean, Philodemus, Epicurus’s custom was to celebrate ‘the Twentieth with distinguished companions after decorating the house with the fruits of the season and inviting everyone to feast themselves.’ Classicist Disking Clary […] has translated a written invitation by Epicurus welcoming all sympathizers to the feast—‘all those who are members of his household and he asks them to exclude none of the ‘outsiders’ who are well disposed to him and friends.’ In the normal Greek household, men and women at separately, especially with guests present. The word for dining room, andron, was literally ‘men’s room.’ At sacrifices and open-air meals, men and women divided into their respect circles […]. Philosophical gatherings were generally all-male affairs. Strikingly, the Epicureans dined together. The community’s main writers included Leontion […] Radically, Epicurean meals were the deliberate reason and means for philosophizing.” (Michael Symons, Meals Matter: A Radical Economics Through Gastronomy)
“While he lived, Epicurus established his birthday so that it was solemnly celebrated and in his will he left provisions that this holiday would be perpetuated (the tenth day of Gamelion [January-February]) every year and that on the twentieth day of each month a reunion was to be held of all the companions in philosophy devoted to his memory and that of Metrodorus (and this came to be called the feast of the Twentieth. We know from Pliny the Elder that in the first century of the CE the Epicurenas still celebrated these two occasions, exactly as Epicurus established them: ‘The offer sacrifices on his birthday, and keep his festival, which they call the eikas [eikas] on the 20th day of every month ….” (Giovanni Realse and John R. Catan, A History of Ancient Philosophy: The schools of the Imperial Age 40)