A fairly standard approach to mathematical Platonism might start with the observation that any circle actually drawn is not a true circle; and one can imagine or have in mind a perfect circle - a universal circle, say; this is taken from Platos theory of Forms or Universals.
This is quite easy to actually imagine, but it does not remain the case, at least for me, when I consider numbers: here, there is two bottles, three stones, or five pebbles; yet I cannot imagine - I mean in the sense of visualise - the numbers two, three or five; though I can quite easily work with them.
Should one make a distinction then, between a geometric mathematical Platonism and an arithmetical version? I mean, is one actually made in mathematical platonism?