But does perichōrēsis mean “a circle dance” and does the cognate verb mean “to dance”? The fact is that these terms have nothing to do with dancing. Liddell and Scott indicate that there are two distinct Greek verbs:
perichōreō means to go around. perichōrēsis is defined as ‘rotation’.
perichoreuō means to dance around. No cognate noun is listed.
The root of the verb that is cognate with perichōrēsis is chōreō (“to give way to, make room for, go forward”), not choreuō (“to dance a round, a choral dance”). So there is no warrant for suggesting that perichōrēsis has any connection with dancing in Greek Classical Literature.
Perhaps, though, it may have come to mean this and so the church fathers had this sense in mind when they applied it to the Trinity? A scan of the information revealed in Lampe’s A Patristic Greek Lexicon, however, is not encouraging:
perichōreō means “interchange” when used in reference to the two natures of Christ and “interpenetrate” when it describes the actions of the members of the Trinity. A similar range of meaning is found for the cognate noun.
perichoreuō is also listed with the meaning “dance round”, but the primary references are found in Pseudo-Dionysius Aeropagita (5th century) and these uses are not related to the Trinity per se. Also, Lampe only lists three occurrences, whereas for perichōreō he lists many occurrences, both Christologically and in relation to Trinitarian discussions.
Again, we find no evidence that suggests perichōreō has anything to do with dancing.
St. John of Damascus (8th century) used perichōrēsis in his Exposition of the Orthodox Faith to describe how the members of the Trinity relate to one another. For example, he says “they are made one not so as to commingle, but so as to cleave to each other and they have their being in each other [kai tēn en allēlais perichōrēsin echousi] without any coalescence or commingling.” However in this context he makes no use of the analogy of dancing to explain this relationship. Augustus Strong indicates that “theologians have designated this intercommunion by the terms perichōrēsis, circumincessio, intercommunication, circulation, inexistentia.”
What can we conclude from this? It seems that some writers have confused perichoreuō (dance round) with perichōreō (interpenetrate). Although the verbs sound similar and are spelled somewhat similarly, they have two quite different meanings. The primary lexica for Classical and Patristic Greek give no indication that perichōreō was ever used to describe the motions of dancing. Catharine LaCugna is right so far as she goes to say that “the philological warrant for this is scant.” It is in fact non-existent.
If a person desires to use the metaphor of dance to describe the mutual interactions of the persons of the Trinity that might be useful and appropriate. However, one cannot justify the use of such a metaphor by trying to connect it with perichōreō. That tune will not play. Nor should one pretend that the term “choreography” in some sense relates to perichōreō. Again, there is no etymological relationship whatsoever. Perichoretic dancing is a modern invention that does not come from the meaning of the underlying Greek term or its use in the Church Fathers.
 George Cladis, Leading the Team-Based Church (San Francisco: Jossey-Bass Publishers, 1999):4.
 Eugene Peterson, Christ Plays in Ten Thousand Places (Grand Rapids, Mich.: Eedrmans, 2005): 44-45
 Catharine LaCugna, God For us: The Trinity and Christian Life (San Francisco: Harper-San Francisco, 1973): 271. Peterson refers to her publication in footnote 15 of his volume and quotes from page 272 as support for his understanding.
 Henry G. Liddell and Robert Scott, A Greek-English Lexicon (Oxford: Clarendon Press, 1966):1394; Montanari, Brill Dictionary of Ancient Greek (2015), 1652; Cambridge Greek Lexicon II (2021), 1126.
 Ibid., 1393. Montanari, Brill Dictionary of Ancient Greek (2015), 1652; Cambridge Greek Lexicon II (2021), 1126.
 G.W.H. Lampe, editor, A Patristic Greek Lexicon (Oxford: Clarendon Press, 1968):1077-1078.
 Augustus Strong, Systematic Theology (Valley Forge, Penn.: Judson Press, 1974):333.
 Op. cit., 271.