Usage: 3 forms in 3 verses
Form Translated As     In Verse(s)
κλιμάκων stairways LXX.Neh.3.15
κλίμαξ stairway LXX.Gen.28.12
κλίμακασ stairways LXX.Neh.12.37

Liddell-Scott-Jones

κλῖμαξ (klimax) a stairway G:N-F

κλῖμαξ, ᾰκος, ,

(κλίνω) ladder (because of its leaning aslant), [Refs]; scaling-ladder, [Refs 5th c.BC+]; προσθεῖναι Th.[same place]; boarding-ladder, gangway, [Refs 5th c.BC+]; κ. σκύτιναι, στύππιναι, [Refs 3rd c.BC+]

__2 staircase, [Refs 8th c.BC+] winding stair, [Refs 3rd c.BC+]
__II frame with crossbars, on which persons to be tortured were tied, [Refs 5th c.BC+]
__II.2 ladder used in reducing dislocations, [Refs 5th c.BC+]
__III wrestler's trick, ἀμφίπλεκτοι κ. [Refs 5th c.BC+]
__IV in Rhet., climax, [Refs 4th c.BC+]
__V part of a chariot, narrowing like steps, [Refs 2nd c.AD+]
__VI in plural, handrails on either side of a bridge, [Refs 2nd c.AD+]