'polygonal' is formed in English by adding the adjectival suffix '-al' to 'polygon', which ultimately comes from Greek 'polýgonon' (from 'polús' meaning 'many' + 'gōnía' meaning 'angle').

'polygon' entered English via Medieval Latin and Old French (cf. Middle French 'polygone'), originating in Greek 'polýgonon'; the modern English adjective 'polygonal' arose by attaching '-al' to the noun 'polygon'.

Initially the root referred to a 'many-angled figure' in Greek; over time the adjective form came to mean 'having the characteristics of a polygon' and remains close to that original sense.