Symmetrical Letter Patterns

We take for granted the symmetrical letter patterns in palindromes - such as LEVEL and KAY AK. These involve all the letters in the world. But what about symmetrical letter patterns which occur in non-palindromic words, such as that of the letter N in ENCHANTMENT? In Making the Alphabet Dance, Ross Eckler gave the name \u27cadence\u27 to a set of identical letters spaced at equal intervals in a word - as in SYNGENESIOTRANSPLANTATION. Her, I add two constraints: the letters must be symmetrical within the word, as well as in relation to each other