Group and Group Isomorphism in Pyraminx
DOI:
https://doi.org/10.20956/j.v20i2.30320Keywords:
Group, S36 symmetry permutation group, subgroup, isomorphism, PyraminxAbstract
Pyraminx is a twisty puzzle in the shape of a tetrahedron with 4 sides. Pyraminx is played with the bottom completely flat and the front side facing the person holding the Pyraminx. The goal of the Pyraminx game is to randomize the colors, then return the scrambled colors to their original color positions by rotating the sides. This research does not discuss the most effective way of solving Pyraminx but focuses more on proving that movements in Pyraminx form group and that there is a group isomorphism from the group of Pyraminx movements to the symmetry permutation subgroup in Pyraminx. First, it is proved that movements in Pyraminx form group using 2 methods, namely direct proof in Pyraminx (Pyaminx movement group) and performing permutations in set containing numeric labels in the form of numbers 1 to 36 on Pyraminx facets by following the movements of Pyraminx ( symmetry permutation subgroup). Furthermore, it is proved that there is a group isomorphism from the Pyraminx movement group to the symmetry permutation subgroup in Pyraminx.
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