Should it not be い かい as I thought the counter for floors was -kai ?
Because of 促音便, the pronunciations of いち, ろく, はち, じゅう, ひゃく change to いっ, ろっ, はっ, じゅっ/じっ, ひゃっ when followed by some counters, like this:
いち + かい → いっかい (1回/1階)
ろく + かい → ろっかい
はち + かい → はっかい
じゅう + かい → じゅっかい
ひゃく + かい → ひゃっかい
いち + こ → いっこ (1個)
ろく + ひき → ろっぴき (6匹)
はち + ほん → はっぽん (8本）
じゅう + ふん → じゅっぷん/じっぷん (10分)
いち + てん → いってん (1点) -- but 6点, 100点 are ろくてん, ひゃくてん
はち + さい → はっさい (8歳) -- but 6歳, 100歳 are ろくさい, ひゃくさい
It is a phonetic transformation similar in English to "aren't".
Instead of saying "are not", you can say "aren't".
Instead of saying "いちかい", you say "いっかい".
The difference is that in Japanese the pronunciation is not optional. You have to say いっかい. It is wrong to say いちかい.
Most of these words are listed in dictionaries and in good grammar books.