EKSPLORASI GRUP DIHEDRAL PADA ORNAMEN MASJID MUNGSOLKANAS BANDUNG
DOI:
https://doi.org/10.24127/ajpm.v15i3.16789Keywords:
Etnomatematika, grup dihedral, Masjid Mungsolkanas, ornamen masjidAbstract
Matematika sering dipandang sebagai ilmu yang abstrak dan terpisah dari kehidupan sehari-hari, sehingga keterkaitannya dengan budaya sering kurang disadari. Padahal, matematika hadir dalam berbagai bentuk budaya, salah satunya melalui pola geometri pada ornamen masjid. Pola-pola tersebut menunjukkan keteraturan yang dapat dianalisis menggunakan konsep teori grup untuk mengungkap struktur matematis yang terkandung di dalamnya. Penelitian ini bertujuan untuk mengeksplorasi struktur grup dihedral pada ornamen Masjid Mungsolkanas Bandung. Metode yang digunakan dalam penelitian ini adalah etnografi, dengan lokasi penelitian di Masjid Mungsolkanas, Bandung, Jawa Barat, Indonesia. Kerangka kerja etnomatematika ini menggunakan empat pertanyaan kunci, yaitu: “Dari mana pengamatan dilakukan?”, "Bagaimana proses pengamatan dilakukan?”, "Apa hasil pengamatan tersebut?”, dan “Apa artinya?”. Peneliti berperan sebagai instrumen utama dalam pengumpulan data melalui teknik triangulasi, yaitu wawancara, observasi, dan studi pustaka. Analisis data dilakukan dalam tiga tahap, yaitu reduksi data, penyajian data, dan penarikan kesimpulan. Hasil penelitian menunjukkan bahwa ornamen Masjid Mungsolkanas mengandung struktur grup dihedral D6. Temuan ini menunjukkan adanya keterkaitan antara nilai estetika ornamen Masjid Mungsolkanas dengan representasi konsep aljabar dalam budaya lokal. Hasil penelitian ini tidak hanya memperluas kajian matematika, tetapi juga memperkuat perspektif etnomatematika melalui eksplorasi pola dan struktur matematis pada ornamen masjid. Dengan demikian, konsep matematika yang bersifat abstrak dapat dipahami dalam konteks budaya yang lebih nyata dan terintegrasi dengan kearifan lokal.
Mathematics is often viewed as an abstract discipline disconnected from everyday life, so its connection to culture is frequently overlooked. In fact, mathematics is present in various cultural forms, one of which is through the geometric patterns found in mosque ornamentation. These patterns exhibit regularities that can be analyzed using concepts from group theory to reveal the mathematical structures they contain. This study aims to explore dihedral group structures in Mungsolkanas Bandung Mosque ornamentation. The method used in this study is ethnography, with the research site located at the Mungsolkanas Mosque in Bandung, West Java, Indonesia. This ethnomathematics framework employs four key questions: “From where is the observation made?”, “How is the observation process conducted?”, “What are the results of the observation?”, and “What does it mean?”. The researcher serves as the primary instrument in data collection through triangulation techniques, namely interviews, observation, and literature review. Data analysis was conducted in three stages: data reduction, data presentation, and drawing conclusions. The research results indicate that the ornaments of the Mungsolkanas Mosque contain a D6 dihedral group structure. This finding suggests a connection between the aesthetic value of the Mungsolkanas Mosque’s ornaments and the representation of algebraic concepts within local culture. The results of this study not only expand the scope of mathematical research but also strengthen the ethnomathematics perspective through the exploration of mathematical patterns and structures in mosque ornamentation. Thus, abstract mathematical concepts can be understood within a more tangible cultural context and integrated with local wisdom.
References
Aboufadil, Y., Thalal, A., Raghni, M. A. E. I., Jali, A., & Oueriagli, A. (2019). Varieties of 12-Fold Rosettes and their Applications in Moroccan Geometric Ornament. Journal of Applied Crystallography, 52(3), 605–617. https://doi.org/10.1107/S1600576719004928
Ahmad, M., Rashid, K., & Naz, N. (2018). Study of the Ornamentation of Bhong Mosque for the Survival of Decorative Patterns in Islamic Architecture. Frontiers of Architectural Research, 7(2), 122–134. https://doi.org/10.1016/j.foar.2018.03.004
Aikenhead, G. S. (2021). Resolving Conflicting Subcultures within School Mathematics: Towards a Humanistic School Mathematics. Canadian Journal of Science, Mathematics and Technology Education, 21(2), 475–492. https://doi.org/10.1007/s42330-021-00152-8
Alani, M. W. (2018). Algorithmic Investigation of the Actual and Virtual Design Space of Historic Hexagonal-Based Islamic Patterns. International Journal of Architectural Computing, 16(1), 34–57. https://doi.org/10.1177/1478077118763237
Albert, F., Gómis, J. M., Blasco, J., Valiente, J. M., & Aleixos, N. (2015). A New Method to Analyse Mosaics Based on Symmetry Group Theory Applied to Islamic Geometric Patterns. Computer Vision and Image Understanding, 130, 54–70. https://doi.org/10.1016/j.cviu.2014.09.002
Ansaroudi, F. N., Kroll, D., Charles, P., & Burry, J. (2026). Geometric Feasibility of Kinetic Islamic Geometric Patterns: A Case Study of Ten-Point Star Configurations in Five Mosques in Isfahan, Iran. Nexus Network Journal, 28(1), 89–119. https://doi.org/10.1007/s00004-025-00848-6
Baysal, A. F., & Ertunç, Ç. Ö. (2025). Reflections of the Interior Ornamentation of Al-Aqsa Mosque and the Dome of the Rock on Islamic Art in the Context of Environmental and Periodical Factors. Filistin Araştırmaları Dergisi, (18), 78–116. https://doi.org/10.34230/fiad.1761130
Bier, C. (2008). Art and Mithāl : Reading Geometry as Visual Commentary. Iranian Studies, 41(4), 491–509. https://doi.org/10.1080/00210860802246176
Chen, X. (2022). Core of Abstract Algebra: Group Theory. In C.-H. Chen, X. Ye, & H. M. Srivastava (Eds.), 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022), 1225927. SPIE. https://doi.org/10.1117/12.2639400
Dewi, R., Hanun, F., Hadiana, D., Sylvia, N., & Ramdani, Z. (2025). Silih Asah, Silih Asih, and Silih Asuh (SILAS): A Decolonial Conceptual Framework for Relational Early Childhood Education in the Sundanese Context amid Global Childhood Discourses. Global Studies of Childhood, 1–13. https://doi.org/10.1177/20436106251398516
Ernest, P. (2016). Mathematics and Values. In B. Larvor (Ed.), Mathematical Cultures: The London Meetings 2012-20144 (pp. 189–214). Springer. https://doi.org/10.1007/978-3-319-28582-5_12
Fajriah, N., & Suryaningsih, Y. (2021). Ethnomathematics of the Jami Mosque Jingah River as a Source Mathematics Learning. Journal of Physics: Conference Series, 1760(1), 012025. https://doi.org/10.1088/1742-6596/1760/1/012025
Firmansyah, A., Nugroho, R., Wahyudi, M. R., Marhayati, & Susanti, E. (2025). Geometric Transformation Concept in Sunan Ampel Surabaya Gate Ornaments. AIP Conference Proceedings 3446, 030032. https://doi.org/10.1063/5.0308601
Ghouchani, M., Gholizade, F., & Sobouti, H. (2023). Geometric Patterns Used in the Architecture of Kaboud Mosque in Tabriz, Iran. Gazi University Journal of Science, 36(3), 984–999. https://doi.org/10.35378/gujs.1055129
Halim, E. A., Hartanti, M., Wianto, E., Lukman, C. C., & Joneurairatana, E. (2024). Investigation of Mathematical Ideas on Drawing Ramakien and Ramayana by Thai and Indonesian Students. The International Journal of Design Education, 18(2), 149–166. https://doi.org/10.18848/2325-128X/CGP/v18i02/149-166
Hayes, L., & Jung, Y. (2023). Beyond Methods: A Model for Teaching Theory in Applied Anthropology. Annals of Anthropological Practice, 47(1), 20–34. https://doi.org/10.1111/napa.12194
Ibrahim, M., & Ch, R. K. (2024). The Importance of Mathematical Thinking in the Classroom: A Theoretical Analysis. In R. K. Hamdan, A. Hamdan, B. Alareeni, & R. El Khoury (Eds.), Information and Communication Technology in Technical and Vocational Education and Training for Sustainable and Equal Opportunityy (Vol. 39, pp. 203–210). Springer. https://doi.org/10.1007/978-981-99-7798-7_17
Loukid, A., ChahamI, K. R., Bahjaoui, T., & BensallamI, S. (2023). Contribution to the study of muqarnas in the mosques of Marrakech. Sustainable Mediterranean Construction, (18), 50–57.
Mania, S., & Alam, S. (2021). Teachers’ Perception toward the Use of Ethnomathematics Approach in Teaching Math. International Journal of Education in Mathematics, Science and Technology, 9(2), 282–298. https://doi.org/10.46328/ijemst.1551
Mansour, O., & Netti, R. (2020). The Arabic Calligraphy: An Identifying Parameter in Space, Time and Contents. In J. Kacprzyk (Ed.), Advances in Intelligent Systems and Computing (Vol. 1140, pp. 313–329). Springer. https://doi.org/10.1007/978-3-030-41018-6_27
Marmur, O. (2023). Numerate Life for Whom? A Non-book-review of John Allen Paulos’s A Numerate Life: A Mathematician Explores the Vagaries of Life, His Own and Probably Yours. The Mathematics Enthusiast, 20(1–3), 51–64. https://doi.org/10.54870/1551-3440.1590
Muhammad, H., Susilowati, L., & Fatmawati. (2020). The Proof of Properties of Dihedral Group and its Commutative Elements. Journal of Physics: Conference Series, 1494(1), 012003. https://doi.org/10.1088/1742-6596/1494/1/012003
Munthe-Kaas, H. Z. (2016). Groups and Symmetries in Numerical Linear Algebra. In J. M. Morel, B. Teissier, & M. Brion (Eds.), Lecture Notes in Mathematics (Vol. 2173, pp. 319–406). Springer Verlag. https://doi.org/10.1007/978-3-319-49887-4_5
Naserabad, A. A., & Ghanbaran, A. (2023). Presenting a Method to Generate Existing and Novel Girihs (Islamic Geometric Patterns) for All Systems and Families Based on 7-Fold Patterns. Computer-Aided Design, 154, 1–13. https://doi.org/10.1016/j.cad.2022.103418
Ouazene, Z., Benslimane, R., & Khamjane, A. (2022). CAD Geometry for the Traditional Tastir Style Moroccan and Andalusian 16-Fold Rosettes. Symmetry: Culture and Science, 33(1), 55–68. https://doi.org/10.26830/symmetry_2022_1_055
Payadnya, I. P. A. A., Atmaja, I. M. D., Noviyanti, P. L., Wibawa, K. A., & Jayantika, I. G. A. N. T. (2025). Exploring “Wa Pat Nem Tus Dasa”: The Potential of a Balinese Traditional Mod 2 Counting System in Culturally Based Mathematics Learning. Journal for Multicultural Education, 19(4), 448–459. https://doi.org/10.1108/JME-02-2025-0050
Pourmahmoud, S., & Fahimifar, A. (2024). A Study on the ‘Philosophy of Decoration’ in the Seljuk Period (5th to 6th Centuries CE) Emphasizing the Dome of ‘Taj Al- Molk’ of the Isfahan Grand Mosque. Vestnik of Saint Petersburg University. Philosophy and Conflict Studies, 40(2), 353–364. https://doi.org/10.21638/spbu17.2024.215
Pramulia, P., Yustitia, V., Kusmaharti, D., Fanny, A. M., & Oktavia, I. A. (2025). Ethnomathematics of Al Akbar Mosque Surabaya: Augmented Reality Comics to Improve Elementary School Students’ Literacy and Numeracy. Multidisciplinary Science Journal, 7(6), 1–13. https://doi.org/10.31893/multiscience.2025277
Purniati, T., Turmudi, Juandi, D., & Suhaedi, D. (2022). Ethnomathematics Study: Learning Geometry in the Mosque Ornaments. International Journal on Advanced Science, Engineering and Information Technology (IJASEIT), 12(5), 2096–2104. https://doi.org/https://doi.org/10.18517/ijaseit.12.5.17063
Purniati, T., Turmudi, & Suhaedi, D. (2020). Ethnomathematics: Exploration of a Mosque Building and its Ornaments. Journal of Physics: Conference Series, 1521(3). https://doi.org/10.1088/1742-6596/1521/3/032042
Purniati, T., Turmudi, T., Juandi, D., & Suhaedi, D. (2021). Ethnomathematics Exploration of the Masjid Raya Bandung Ornaments in Transformation Geometry Materials. Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang, 5(2), 235–243. https://doi.org/10.31331/medivesveteran.v5i2.1639
Radiusman, Novitasari, S., Nurmawanti, I., Fauzi, A., & Simanjuntak, M. (2021). Ethnomathematics: Mathematical Values in Masjid Agung Demak. AIP Conference Proceedings 2331, 1–7. https://doi.org/10.1063/5.0041639
Rashdan, W., & Ashour, A. F. (2022). Aesthetic Interpretation for Islamic Geometry in Interior Design. WIT Transactions on the Built Environment, 89–101. https://doi.org/10.2495/IHA220071
Rezqi, N., & Furqan, A. (2025). Nilai-nilai Budaya Sunda Trisilas (Silih Asih, Silih Asah, Silih Asuh) dalam Perspektif Al-Qur’an. Indonesian Journal of Research in Islamic Studies, 2(2), 85–93. https://doi.org/10.64420/ijris.v2i2.335
Setyawan, D., Bulkani, & Herman. (2026). The Influence of Realistic Mathematics Education Supported by Batang Garing Philosophy on Students’ Conceptual Understanding of the Greatest Common Factor. Multidisciplinary Science Journal, 8(9), 2026452. https://doi.org/10.31893/multiscience.2026452
Shaw, W. M. K. (2022). Islamic Geometries: Spiritual Affects Against a Secularist Grid. Sophia, 61(1), 41–59. https://doi.org/10.1007/s11841-022-00905-4
Soliana, W. M. Z. W., Marzuki, I., Rushana, S., & Hafiza, G. N. (2021). The Symmetry Analysis in Sulaiman Esa Paintings through Islamic Art Concept. AIP Conference Proceedings 2347, 1–8. https://doi.org/10.1063/5.0052186
Tang, D., Wang, Z., & Yue, B. (2022). Applications of Group Theory. Journal of Physics: Conference Series, 2381(1), 012110. https://doi.org/10.1088/1742-6596/2381/1/012110
Turan, Y. (2025). Architectural Element of the Anatolian Seljuk Period – Muqarnas and the Symmetry Story of Muqarnas. Symmetry: Culture and Science, 36(2), 159–174. https://doi.org/10.26830/symmetry_2025_2_159
Vos, P., Wiik, A., & Martinez, P. H. (2024). "Imagine, Maths is Used Anywhere, and We don’t Get to Know this”—Upper Secondary Students and the Relevance of Advanced Mathematics. Frontiers in Education, 9, 1–14. https://doi.org/10.3389/feduc.2024.1338205
Yassine, A. L., Abdelaziz, J., Ahmed, E. O., Thalal, A., Aboufadil, Y., & Elidrissi R, M. A. (2020). New Approach for the Detection of Family of Geometric Shapes in the Islamic Geometric Patterns. IJACSA) International Journal of Advanced Computer Science and Applications, 11(3), 342–348. https://doi.org/https://doi.org/10.14569/IJACSA.2020.0110343
Yosua, A. (2025). Strategi Pendekatan Kontekstual Suku Sunda Melalui Nilai Silih Asah, Silih Asih dan Silih Asuh. The New Perspective in Theology and Religious Studies, 6(1), 035–058. https://doi.org/10.47900/gh2mtd41
Zeilabi, N. (2019). Talismans and Figural Representation in Islam: A Cultural History of Images and Magic. British Journal of Middle Eastern Studies, 46(3), 425–439. https://doi.org/10.1080/13530194.2017.1410466
Zuliana, E., Dwiningrum, S. I. A., Wijaya, A., & Purnomo, Y. W. (2023). The Geometrical Patterns and Philosophical Value of Javanese Traditional Mosque Architecture for Mathematics Learning in Primary School: An Ethnomathematic Study. The Journal of Education, Culture, and Society, 14(2), 512–532. https://orcid.org/0000-0001-6377-6074
Downloads
Published
Issue
Section
License
Copyright (c) 2026 AKSIOMA: Jurnal Program Studi Pendidikan Matematika
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with AKSIOMA: Jurnal Program Studi Pendidikan Matematika agree to the following terms:
Creative Commons License
AKSIOMA: Jurnal Program Studi Pendidikan Matematika is licensed under a Creative Commons Attribution 4.0 International License.
This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. AKSIOMA offers all authors of journal articles allows their research openly available, free access and time restrictions.
All articles published Open Access will be immediately and permanently free for everyone to read and download. Under the CC-BY license, authors retain ownership of the copyright for their article, but authors grant others permission to use the content of publications in AKSIOMA in whole or in part provided that the original work is properly cited. Users (redistributors) of AKSIOMA are required to cite the original source, including the author's names, AKSIOMA as the initial source of publication, year of publication, volume number and DOI (if available).
.png)
.png)
