With the help of computer symbolic manipulation [14], spectral parameter-free solutions to Tetrahedral equation, which is a multi-dimensional generalization of Yang-Baxter Equation by Zamolodchikov[4], are obtained.

With a variational method and a modified arrangmement channel quantum mechanics(MACQM) method,the energies of a equilateral triangle H-3 and a tetrahedron H-4 system are calculated.

Some of the cross sections are used to stand for a centain component, and semiternary phase diagrams are ploted, then a quaternary phase diagram shown in a tetrahedron is obtained.

The results indicate that the tip of this geometry can not only produce focusing spot at nanometer scale but also engender enormous field enhancement under the excitation of plane wave from the base of pyramidal tip.

In order to understand the application of opposite vertical pyramidal tips in single molecule damnification and measuring system,enhancement of opposite vertical pyramidal tips was analyzed and computed.

An effective method of constructing geological model by using tetrahedron;

A New Generation Tetrahedron Mesh Technique of Complex Mining Geological Bodies;

By amending the auxiliary geometric primitive,diagonal,of generalized tri-prism(GTP) into tetrahedron,the inconsistentness of data organization and of geometric primitive in real 3D geosciences modeling as well as the geometric interstice in spatial operation were solved.

After reconstructing ,the common four surfaces planer has many functions such as automatic adjusting cutting tool and automatic machining floors.