The Collaborative International Dictionary of English v.0.48:
Intercommune \In`ter*com*mune"\, v. i. [imp. & p. p. Intercommuned; p. pr. & vb. n. Intercommuning.] [Cf. Intercommon, Intercommunicate, Commune.] [1913 Webster] 1. To intercommunicate. [Obs.] [1913 Webster] 2. To have mutual communication or intercourse by conversation. [Scot.] [1913 Webster]