Is there an sh sound in the middle of polytrichum?
heard as politrishum
spelled polytrichum
No. The ch is said as k, so politrishum has to be written polytrichum.
What the ear did
Two decisions have gone the wrong way at once, i for y and sh for ch. The sh reading of ch belongs to words English took from French, like chalet and chandelier. This one came in from Greek by way of Latin and kept the harder sound.
P-O-L-Y-T-R-I-C-H-U-M
The full entry for polytrichum covers the name itself.