Abstract
In this paper, we explore possible higher-dimensional analogues for the well known chaotic behavior of the sequence of pedal triangles of a given triangle. We start with an orthocentric d-simplex S, i.e., one whose altitudes are concurrent, and we show that its pedal d-simplex, i.e., the one whose vertices are the feet of the altitudes, is orthocentric if and only if S is of the special type known as a d-kite. We then study the periodicity and chaotic behevior of the sequence of shapes of (P-n(K))(a)(n = 1), where K is a d-kite, and where P(K) is the pedal d-kite of K.