Actually, SHA3 was not converted to ternary. The input is simply chunked into 243 trits that are converted to 48 bytes and are absorbed into KECCAK-384. Squeezing works the other way round, 48 bytes are squeezed and converted into 243 trits.
Ah, that's a good point - I was aware of that, but you made me realize that using the word "convert" to describe what they did could give the wrong impression. I've changed my description to say they "wrapped" SHA3.