'astroid' originates from Greek, specifically the word 'astroides', where the element 'astr-' (from Greek 'astron') meant 'star' and the suffix '-oid' (from Greek 'eidos') meant 'form' or 'likeness'.

'astroides' passed into Latin/New Latin formations and was adopted into English as 'astroid' to denote something 'star-like'; in mathematics it came to name the specific four-cusped curve.

Initially it carried the general sense 'star-like' (i.e., resembling a star); over time it became specialized to refer to the particular four-cusped hypocycloid in geometry (and occasionally was used historically as a variant of 'asteroid').