'palindromical' originates from Greek, specifically the word 'palindromos,' where 'palin-' meant 'again' and 'dromos' meant 'running.'

'palindromos' passed into English via Neo-Latin/Modern coinage as 'palindrome' and later formed the adjective 'palindromical' (and variant 'palindromic') by addition of English adjective-forming suffixes.

Initially, the Greek root conveyed the idea of 'running back again'; over time it evolved into the modern linguistic sense of 'reads the same backward and forward.'