word-forming element used freely in English, "between, among, during," from Latin inter (prep., adv.) "among, between, betwixt, in the midst of" (also used extensively as a prefix), from PIE *enter "between, among" (source also of Sanskrit antar, Old Persian antar "among, between," Greek entera (plural) "intestines," Old Irish eter, Old Welsh ithr "among, between," Gothic undar, Old English under "under"), a comparative of root *en "in."
A living prefix in English from 15c. and used with Germanic as well as Latinate words. Spelled entre- in French; most words borrowed into English in that form were re-spelled 16c. to conform with Latin except entertain, enterprise. In Latin, spelling shifted to intel- before -l-, hence intelligence, etc.
1520s, "to impart (information, etc.); to give or transmit (a quality, feeling, etc.) to another," from Latin communicatus, past participle of communicare "to share, communicate, impart, inform," literally "to make common," related to communis "common, public, general" (see common (adj.)). Meaning "to share, transmit" (diseases, etc.) is from 1530s. Intransitive sense, of rooms, etc., "to open into each other" is from 1731. Related: Communicated; communicating.
<a href="https://www.etymonline.com/word/intercommunicate">Etymology of intercommunicate by etymonline</a>
Harper, D. (n.d.). Etymology of intercommunicate. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/intercommunicate