秘密 is a curious word because both characters are pronounced mì yet they are different from each other. Given that there are so many homophonous characters in Chinese, I'm curious if there's any other combinations of them into words, and if not why did 秘密 become the exception?
I've come across words like this a couple of times.
Alliteration (双声) seems to be quite common in Putonghua, and this is an extreme form of alliteration.
It's interesting how all these examples use the fourth tone.
There are more words like this but they tend to be less commonly used or literary words (书面语). Eg: 幽忧 yōuyōu
Edit: Mou某 gave two other good examples: 屈曲 qūqū; 实时 shíshí. And these aren't fourth tone, which is nice.
Edit 2: 全权 quánquán (from Becky 李蓓 's comment)
Edit 3: 意义 yìyì; 意译 yìyì; 异议 yìyì (from Olle Linge's comment)