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We introduce a homomorphism from the quantum affine algebras$U_q(D^{(2)}_{n+1}), U_q(A^{(2)}_{2n}), U_q(C^{(1)}_{n})$ to the $n$-foldtensor product of the $q$-oscillator algebra ${\mathcal A}_q$. Their actioncommute with the solutions of the Yang-Baxter equation obtained by reducing thesolutions of the tetrahedron equation associated with the modular and the Fockrepresentations of ${\mathcal A}_q$. In the former case, the commutativity isenhanced to the modular double of these quantum affine algebras.

Tetrahedron Equation and Quantum $R$ Matrices for modular double of $U_q(D^{(2)}_{n+1}), U_q(A^{(2)}_{2n})$ and $U_q(C^{(1)}_{n})$