Take the word TEA and transfer the last letter to the start, obtaining ATE. Repeat this operation on ATE to get its present tense, EAT. A final transfer returns us to the original word, TEA, completing the cycle. It is not difficult to find other examples using rarer three-letter words; in the July 1975 Games & Puzzles, Darryl Francis exhibited five more based on the letters AIT, ASP, EON, ETH and ICH (all fifteen words can be found in Chambers Twentieth Century Dictionary).
Eckler, A. Ross
Word Ways: Vol. 15
, Article 8.
Available at: https://digitalcommons.butler.edu/wordways/vol15/iss3/8