In our thesis we shall describe the mathematical background of the Pyraminx. Pyraminx is a mechanical puzzle, made of various moveable pieces. One of the Pyraminx challenges is how to return the puzzle to its original position, where there are nine smaller triangles of the same colour on each side of the tetrahedron. Our goal is to find the algorithms for solving the Pyraminx. Our thesis therefore includes the description of the LBL method. Furthermore, we focus on the properties of the Pyraminx position group. We have determined that the possible positions and connections correspond to a particularly group structure. We can determine the Pyraminx position with the triple (^⃑, ^⃑⃑⃑, β), where ^⃑ stands for orientation vector of vertices and centres, where ^⃑⃑⃑ stands for the orientation vector of the edges, and β presents the edge permutation. In the end of the thesis we prove that the Pyraminx group is isomorphic to the group 38 ^ (26⣊^6).
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