  We say a finite word $x$ is a palindromic periodicity if there exist two
palindromes $p$ and $s$ such that $|x| \geq |ps|$ and $x$ is a prefix of the
word $(ps)^\omega = pspsps\cdots$. In this paper we examine the palindromic
periodicities occurring in some classical infinite words, such as Sturmian
words, episturmian words, the Thue-Morse word, the period-doubling word, the
Rudin-Shapiro word, the paperfolding word, and the Tribonacci word, and prove a
number of results about them.
