-μι Verbs

Present Tense Conjugation
(principal part one)

• -υμι: e.g ἀπόλλυμι (to lose; to destroy)
• -ημι: the -η/-α class: e.g. ἱστημι (to make stand) and some others
  -ημι: the -η/-ε class: τίθημι (to set up)
  -ημι: the -η/-ε class: ἵημι (to release, throw, hurl...)
  Why 2 groups? Because η is the long (grade) equivalent of both α and ε
• -ωμι. Only one verb: δίδωμι (to give)
   

1. They are different from -ω verbs in the present tense only! (except for δίδωμι, τίθημι and ἵημι)
2. They attach the personal endings (for I, you, he.....) directly to the stem
3. Their stem vowel is long in the active voice singular of
   i) present indicative,
   ii) imperfect and
   iii) imperative: you (singular) do it! ,
   short everywhere else. With just an active present participle seemingly playing odd man out (long masculine and feminine endings due to contraction of short stem with participle ending, short neuter). See participles of -μι verbs, active present and aorist participles on  this page .
    

• Of course, it is not ἱστάασιν but ἱστᾶσιν. Because α + α contracts to long ᾱ, circumflex ᾶ if stressed. Like here.
• The other difficult child ἵημι (release; hurl) is inflected exactly like τίθημι:
  ἵημι, ἵης, ἵησι, ἵεμεν, ἵετε but ἱᾶσι,
  not ἱέασιν but a normal contraction: έ+α => ᾶ,
  contraction not present nor wanted in τίθημι-τιθέασιν)

*

It should of course be παιδεύ ε σαι.
But, after dropping the intervening σ, παιδευ ε αι contracts quite naturally to either παιδεύει or παιδεύῃ. Thematic vowel incorporated into the contraction!