We notice a remarkable connection between Bazhanov-Sergeev solution of Zamolodchikov tetrahedron equation and certain well-known cluster algebra expression. The transformation is then identified with sequence four mutations. As an application the new formalism we show how to construct integrable system spectral curve arbitrary symmetric Newton polygon. Finally, embed this into double Bruhat cel...

We give a simple proof based on symmetries that there are no geodesics from vertex to itself in the cube, tetrahedron, octahedron, and icosahedron.

Many physical quantities in solid-state physics are calculated from $k$-space summation. For spectral functions, the frequency-dependent factor can be decomposed into energy-conserving $\ensuremath{\delta}$-function part and nondissipative principal value part. A very useful scheme for this summation is tetrahedron method. Tetrahedron methods have been widely used to calculate of part, such as ...