Does the name end -phus or -phis?
heard as rhytidiadelphis
spelled rhytidiadelphus
It ends -phus, from adelphos, so rhytidiadelphis should be rhytidiadelphus.
What the ear did
Latin masculine genus names end in -us, and the vowel is swallowed in speech. If you cannot hear which vowel it is, the safe bet in a Latin name of this shape is u.
R-H-Y-T-I-D-I-A-D-E-L-P-H-U-S
The full entry for rhytidiadelphus covers the name itself.