Why do so many people write polytrikum?
heard as polytrikum
spelled polytrichum
Because that is exactly what the word sounds like. The k sound in the middle is spelled ch: polytrichum.
What the ear did
Greek chi is transliterated ch in Latin and stays ch in English, but it never picked up the sound of church. It is the same ch as in chorus, chemist, chrome, architect and echo, all of them Greek words that came through Latin with the spelling intact and the sound unchanged. English later borrowed a second ch from French, the one in chef and machine, and kept a third of its own in church and chalk. Three sounds now share two letters, and only the source language tells you which is which. Polytrichum is Greek from end to end, from polys, many, to trichos, hair, so the k reading is the right one and the spelling stays ch. It is worth knowing the pattern rather than the word: a Greek plant name with a k sound in the middle almost always hides an h behind the c.
P-O-L-Y-T-R-I-C-H-U-M
The full entry for polytrichum covers the name itself.