In his book "Arnold's Problems", Vladimir Arnold shares a collection of questions without answers formulated during seminars in Moscow and Paris for over 40 years. One of these problems, stated in 1994, goes as follows: Find all projective curves projectively equivalent to their duals. The answer seems to be unknown even in RP².

Motivated by this question, in their paper "Self-dual polygons and self-dual curves" from 2009, D. Fuchs and S. Tabachnikov explore a discrete version of Arnold's question in 2-dimensions. If P is an n-gon with vertices A₁, A₃, ... A_2n-1, then its dual polygon P* has vertices B*₂, B*₄, ... B*_2n, where B*_i is the line connecting the points A_i-1, A_i+1. Given an integer m, a polygon P is m-self-dual if there is a projective transformation f such that f(A_i) = B_I+m.

In this talk, I will generalize Fuchs and Tabachnikov's work to polygons in higher dimensions.