Abstract
The Soma cube is a solid dissection puzzle invented by Piet Hein in 1936, in which seven pieces made out of unit cubes must be assembled into a 3×3×3 cube. The total number of solutions (240) was first enumerated by John H. Conway and Michael J. T. Guy in 1961. The logic behind the enumeration was crafted with SOMAP which is hard to understand. The purpose of this thesis is to convert the puzzle into a mathematical experiment suitable for elementary exploration by finding 10 essential dissections. Once the essential solutions are found we may proceed to discover other new dissections. Since mathematical discoveries are often accompanied by consideration of symmetries, we are to list 5 pairs of such examples. As applications will to discuss how Soma Cube can be integrated into the teaching, so that students hands-on and through discussion, to enhance the mathematical interest and thinking ability. A program to forester innovative thinking both in mathematics competition and in science fair is drafted.