Using Keccak permutation as a block cipher
First, this is a slightly silly exercise because most applications are not well-served by a block cipher in particular but rather by things built out of them, such as authenticated encryption schemes.  Probably the most widely used authenticated encryption scheme today built out of AES, AES-GCM, doesn't even use the inverse direction, and would provide better security bounds if AES were a pseudorandom function family rather than a pseudorandom permutation family.  And there are already perfectly good authenticated encryption schemes built out of Keccak, such as Ketje and Keyak, both submitted to CAESAR.

But let's take the exercise at face value and suppose you really do want a block cipher.  The obvious way to get a block cipher out of Keccak is with a single-key Even–Mansour construction analyzed by Dunkelman, Keller, and Shamir.  Specifically, for a $b$-bit permutation $F$ (standard SHA-3 has $b = 1600$, but there are shorter variants, such as $b = 200$ used by Ketje for environments with tight resource constraints), we can define, for $b$-bit keys $k$, the $b$-bit block cipher $$E_k(m) = F(m \oplus k) \oplus k.$$  Since collision-resistance is not relevant to this application, instead of the standard $\operatorname{Keccak-\mathit{f}}[b] = \operatorname{Keccak-\mathit{p}}[b, n_r]$ permutation where $n_r = 12 + 2\log_2 (b/25)$ is the standard number of rounds, we might consider a much smaller number $n_r$ of rounds, as you will find Ketje and Keyak use.

Maybe a 1600-bit key seems excessive for a standard 128-bit security level.  Maybe you could make do with a smaller key, padding it with zeros, $$E_k(m) = F(m \oplus (k \mathbin\Vert 0^{b - 256})) \oplus (k \mathbin\Vert 0^{b - 256}).$$  I haven't done the analysis of a padded-key variant of Even–Mansour; maybe if you read the Dunkelman, Keller, and Shamir paper you'll find an obvious answer.  But we can always derive longer keys from shorter keys using standard functions like HKDF, or even Keccak-based ones like SHAKE256 or KMAC.  So unless you have an amazingly constrained application requiring (a) squeezing out those last few cycles, and (b) a novel Keccak-based block cipher, those cycles are probably not worth the effort to figure out the detailed security analysis!  Thus I leave it as an extra-credit exercise for the reader which will not affect your standard grade.