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.
References
Abdy, M., Sukarna & Safitri, N. H., 2018. Isomorfisma Grup pada Rubik
Revenge. Skripsi. Universitas Negeri Makassar, Makassar.
Bhattacharya, P. B., Jain, S. K. & Nagpaul, S. R. 1995. Basic Abstract Algebra Second Edition. United Kingdom: Cambridge University Press.
Brata, A. 2010. Langkah Mudah Menjadi Master Rubik. Jakarta: Bukune.
Chen, J. 2004. Group Theory and the Rubik’s Cube.
Erawaty, N. & Amir, A. K. 2016. Struktur Aljabar. Universitas Hasanuddin: Pusat Kajian Media dan Sumber Belajar LKPP.
Fraleigh, J. B. & Brand N. E. 2021. A First Course in Abstract Algebra Eighth Edition. Hoboken: Pearson Education.
Gu, Y., 2023. Introduction of Several Special Groups and Their Applications to Rubik’s Cube. Highlights in Science, Engineering and Technology, 47, 172–175. https://doi.org/10.54097/hset.v47i.8186
https://www.worldcubeassociation.org/regulations/translations/indonesian/#article- 12-notation. (diakses 3 Desember 2022)
Hu, W., 2023. Applying the Group Theory to Rubik’s Cube. Highlights in Science, Engineering and Technology, 47, 122–125. https://doi.org/10.54097/hset.v47i.8174
Ihsan, M. K., Haryanto, L. & Erawaty, N., 2016. Aksi Grup dalam Pembentukan Homomorfisma pada Rubik’s Cube. Skripsi. Universitas Hasanuddin, Makassar.
Joyner, D. 2008. Adventures in Group Theory: Rubik’s Cube, Merlin’s Machine, and Other Mathematical Toys. Earth Island Institute.
Judson, T. W. 2014. Abstract Algebra Theory and Applications. Stephen F. Austin State University.
Kurnianingtyas, D. T., Mas’oed, T. W. & Aliatiningtyas, N., 2012. Grup dan Homomorfisma Grup pada Rubik Revenge. Skripsi. Institut Pertanian Bogor, Bogor.
Lyu, Z., Liu, Z., Khojandi, A., & Yu, A. J., 2022. Q-learning and Traditional Methods on Solving the Pocket Rubik’s Cube. Computers & Industrial Engineering, Volume 171, 108452, ISSN 0360-8352, https://doi.org/10.1016/j.cie.2022.108452.
Rotman, J. J. 2003. Advanced Modern Algebra. Prentice Hall Inc.
Sharma, R. K., Shah, S. K. & Shankar, A. G. 2011. Algebra 1 A Basic Course in Abstract Algebra. India: Pearson Education in South Asia.
Sikiric, M. D., 2020. A Variation on the Rubik's Cube. Proceedings of the 3rd Croatian Combinatorial Days. https://doi.org/10.5592/CO/CCD.2020.03
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Author and publisher
This work is licensed under a Creative Commons Attribution 4.0 International License.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Jurnal Matematika, Statistika dan Komputasi is an Open Access journal, all articles are distributed under the terms of the Creative Commons Attribution License, allowing third parties to copy and redistribute the material in any medium or format, transform, and build upon the material, provided the original work is properly cited and states its license. This license allows authors and readers to use all articles, data sets, graphics and appendices in data mining applications, search engines, web sites, blogs and other platforms by providing appropriate reference.
