  Bethe Ansatz was discoverd in 1932. Half a century later its algebraic
structure was unearthed: Yang-Baxter equation was discovered, as well as its
multidimensional generalizations [tetrahedron equation and $d$-simplex
equations]. Here we describe a universal method to solve these equations using
Clifford algebras. The Yang-Baxter equation ($d=2$), Zamalodchikov's
tetrahedron equation ($d=3$) and the Bazhanov-Stroganov equation ($d=4$) are
special cases. Our solutions form a linear space. This helps us to include
spectral parameters. Potential applications are discussed.
