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**Ateneo Symmetries in Algebra and Geometry Laboratory**

The research group focuses on the fields of group theory, mathematical crystallography, and discrete geometry. Current research topics include geometric and crystallographic groups, tilings and polytopes, and symmetries in nature and culture. We give an emphasis on the interplay between algebraic and geometric objects in our research.

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**Current Members**

Ma. Louise Antonette N. De Las Peñas (Head)

Mark L. Loyola (PhD Math, 2016; MS Math, 2011)

Agatha Kristel M. Abila (PhD Math candidate; MS Math, 2019)

Nonie Elvin S. Leyrita (PhD Math candidate)

Kristan B. Liza (PhD Math candidate; MS Math, 2018)

Mark Camilo C. Mamaril (PhD Math candidate; BS Math, 2014)

April Lynne D. Say-awen (PhD Math, 2016)

Eduard C. Taganap (PhD Math, 2017), Central Luzon State University

Mark D. Tomenes (PhD Math, 2021; MS Math, 2018)

Jonn Angel L. Aranas (MS Math, 2021)

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**Former Members**

Paolo B. Araune (MS Math, 2018)

Enrico Paolo Bugarin (MS Math, 2008)

Ma. Carlota Decena (PhD Math, 2007)

Grace M. Estrada (PhD Math, 2017)

Ele Gealogo (BS Math, 2017)

Beaunonie Gozo, Jr (PhD Math, 2010)

Glenn R. Laigo (PhD Math, 2008; MS Math 2005)

Eden Delight P. Miro (PhD Math, 2009; MS Math 2006)

Eko Budi Santoso (MS Math, 2013)

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**Cooperations**

Dr. Antonio Basilio, Ateneo de Davao University

Dr. Dirk Frettlöh, Bielefeld University, Germany

Dr. Yasushi Gomi, Sophia University, Japan

Dr. Egon Schulte, Northeastern University, USA

Dr. Marjorie Senechal, Smith College, USA

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**Publications**

1. Tomenes, M. and De Las Peñas, M. L. A. N. k-isotoxal tilings from [pn] tilings. Journal of Mathematics and the Arts, in press.

2. Say-awen, A. L., Frettlöh, D. and De Las Peñas, M. L. A. N. On Frequency Module of the Hull of a Primitive Substitution Tiling. Acta Cryst A78-1 (2022),1-20.

3. De Las Peñas, M. L. A. N. and Taganap, E. Crystallographic Flat Origami from n-uniform tilings. Discrete and Computational Geometry, Graphs and Games (eds, J. Akiyama, et al), JCDCGGG 2018, LNCS 13034, Springer Nature Switzerland (2021), 136-151.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/170/

4. De Las Peñas, M. L. A. N. Mathematical Sightings at the Museum of Tomorrow. The Mathematical Intelligencer 42-1 (2020), 24-28.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/115/

5. Aranas, A. and Loyola, M.L. Geometric Realizations of Abstract Regular Polyhedra with Automorphism group H3. Acta Cryst A76-3 (2020), 358-368.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/143/

6. Abila, A.K, De Las Peñas, M. L. A. N. and Taganap, E. Local and Global Color Symmetries of a Symmetrical Pattern. Acta Cryst A75 (2019), 730-745.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/116/

7. Taganap, E. and De Las Peñas. M. L. A. N. k-Isocoronal Tilings. Acta Cryst A 75 (2019) 94-106.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/48/

8. Say-awen,A. L., Frettlöh, D. and De Las Peñas, M. L. A. N. Primitive Substitution Tilings with Rotational Symmetries. Acta Cryst A 74 (2018), 388-398.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/16/

9. Taganap, E. and De Las Peñas, M. L. A. N. Hyperbolic Isocoronal Tilings. Journal of Mathematics and the Arts 12:2-3 (2018), 96-110.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/12/

10. Loyola, M. L., Gomi, Y. and De Las Peñas, M. L. A. N. String C-Groups of Order 1024. Contributions to Discrete Mathematics 13-1 (2018), 1-22.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/44/

11. Frettlöh, D. Say-awen, A. L. and De Las Peñas, M. L. A. N. Substitution Tilings with Dense Tile Orientations and n-fold Rotational Symmetry. Indagationes Mathematicae 28 (2017), 120-131.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/11/

12. Mamaril, M. C. and De Las Peñas, M. L. A. N. The Lamplighter Group Ln(h). AIP Conference Proceedings: 7th SEAMSUGM International Conference on Mathematics and its Applications 2015 1707, 020011 (2016); doi: 10.1063/1.4940812

link: https://archium.ateneo.edu/mathematics-faculty-pubs/24/

13. Loyola, M. L., De Las Peñas, M. L. A. N, Estrada, G. and Santoso, E. B. Symmetry Groups Associated with Tilings on a Flat Torus.Acta Cryst A 71 (2015), 99-110.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/8/

14. Say-awen, A. L., De Las Peñas, M. L. A. N and Rapanut, T. On Color Fixing Groups Associated with Colored Symmetrical Tilings. AIP Conference Proceedings: International Conference on Mathematics, Engineering and Industrial Applications 2014 1660, 050012 (2015); doi:10.1063/1.4915645

link: https://archium.ateneo.edu/mathematics-faculty-pubs/23/

15. Taganap, E., De Las Peñas, M. L. A. N. and Rapanut, T. Crystallographic Flat Origami with Three Flat Foldability Types of the Generating Unit.AIP Conference Proceedings: International Conference for Mathematical Sciences 2014, 1602, 662 (2014); doi: 10.1063/1.4882556

link: https://archium.ateneo.edu/mathematics-faculty-pubs/40/

16. Loyola, M. L., De Las Peñas, M. L. A. N, Estrada, G. and Santoso, E. B. A Quotient Space Approach to Model Nanotori and Determine their Symmetry Groups. AIP Conference Proceedings: International Conference for Mathematical Sciences 2014, 1602, 620 (2014); doi: 10.1063/1.4882549

link: https://archium.ateneo.edu/mathematics-faculty-pubs/41/

17. Loyola, M. L., De Las Peñas, M. L. A. N, Basilio, A. and Santoso, E. B. Symmetry Groups of Single Wall Nanotubes. Acta Cryst A 70 (2014), 12-23.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/42/

18. Provido, E. B., De Las Peñas, M. L. A. N. and Felix, R. P. On Subgroups of Crystallographic Coxeter Groups. Acta Cryst. A 69 (2013), 445-451.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/31/

19. Bugarin, E. P., De Las Peñas, M. L. A. N. and Frettlöh, D. Perfect Colourings of Cyclotomic Integers. Geometria Dedicata 162 (2013), 271-282.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/27/

20. Loyola, M. L., De Las Peñas, M. L. A. N. and Basilio, A. Colorings of Single Wall Carbon Nanotubes. Zeitschrift für Kristallographie 227 (2012), 672-680.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/38/

21. Bugarin, E. P. and De Las Peñas, M.L.A.N. On Bravais Colorings Associated with Periodic and Non-Periodic Crystals. Phil. Journal of Science 140-1 (2011), 89-97.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/99/

22. Bugarin, E. P., De Las Peñas, M.L.A.N and Frettlöh, D. Colourings of Cyclotomic Integers with Class Number One. Philosophical Magazine 91:19-21 (2011), 2690-2699.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/101/

23. Gozo, B., De Las Peñas, M.L.A.N., Laigo, G. R. and Felix, R. P. Semi-Perfect Colourings of Hyperbolic Tilings. Philosophical Magazine 91:19-21 (2011), 2700-2708.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/102/

24. Laigo, G. R., De Las Peñas, M.L.A.N. and Felix, R. P. On Subgroups of Hyperbolic Coxeter Tetrahedral Groups. Zeitschrift für Kristallographie 225 (2010), 313-338.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/136/

25. Bugarin, E. P., De Las Peñas, M.L.A.N., Evidente, I., Felix, R. P and Frettlöh. D. On Color Groups of Bravais Colorings of Planar Modules with Quasicrystallographic Symmetries. Zeitschrift für Kristallographie 223: 11-12 (2008), 785-790.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/104/

26. Decena, C., De Las Peñas, M.L.A.N. and Felix, R. P. Enumeration of Index 3 and 4 Subgroups of Hyperbolic Triangle Symmetry Groups. Zeitschrift für Kristallographie 223 10 (2008), 543-551.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/105/

27. De Las Peñas, M.L.A.N. and Felix, R. P. Color Groups Associated with Square and Hexagonal Lattices. Zeitschrift für Kristallographie 222 (2007), 505-512.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/107/

28. Provido, E. B., De Las Peñas, M.L.A.N. and Felix, R. P. On Index 2 Subgroups of Hyperbolic Symmetry Groups. Zeitschrift für Kristallographie 222 (2007), 443-448.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/108/

29. Laigo, G.R., De Las Peñas, M.L.A.N. and Felix, R. P. Colorings of Hyperbolic Plane Crystallographic Patterns. Zeitschrift für Kristallographie 221 (2006), 665-672.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/110/

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**Non-Scopus Publications List**

1. Tomenes, M. and De Las Peñas, M.L.A.N. Tilings with Congruent Edge Coronae. Polytopes and Discrete Geometry: Contemporary Mathematics Series, (eds G. Cunningham, M. Mixer and E. Shulte), American Mathematical Society (2021), 251-272.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/142/

2. Taganap, E. and De Las Peñas, M.L.A.N. Color Symmetry Approach to the Construction of Crystallographic Flat Origami.Origami6 (eds. P.Wang-Iverson, R.Lang, etal), American Mathematical Society (2015), 11-20.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/26/

3. De Las Peñas, M.L.A.N., Baylas, N. IV and Rapanut, T. Weaving Symmetry of the Philippine Northern Kankana-ey. Bridges Towson: Mathematics, Music, Art, Architecture and Culture (eds. R. Bosch, D. Mckenna and R. Sarhangi), Tessellations Publishing, Arizona (2012), 267-274.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/39/

4. Provido, E.B., De Las Peñas, M.L.A.N. and Decena, C. On the Subgroups of the Triangle Group ∗2p(infinity). Advances in Algebraic Structures (eds. W. Hemakul et al), World Scientific Co. Ltd (2012), 478-495.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/100/

5. Provido, E. B., De Las Peñas, M.L.A.N. and Felix, R. P. On Torsion Free Subgroups of p32 and Related Colored Tilings.Bridges Pécs: Mathematics, Music, Art and Architecture (eds. G. Hart and R. Sarhangi),Tessellations Publishing, Arizona (2010), 410-419.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/103/

6. Laigo, G. R., De Las Peñas, M.L.A.N. and Felix, R. P. Coloring Uniform Honeycombs. Bridges Banff: Mathematics, Music, Art and Culture (eds. C.Kaplan and R. Sarhangi), Tarquin Books, Hertfordshire (2009),131-138.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/129/

7. Decena, C. and De Las Peñas, M. L. A. N. On Orbifolds Associated with Subgroups of Triangle Groups of Index at most Four. Loyola Schools Review: Science and Engineering 8 (2009), 63-84.

8. De Las Peñas, M.L.A.N. , Laigo, G. R. and Puzon, I. Coxeter Groups in Colored Tilings and Patterns. Bridges Leeuwarden: Mathematical Connections in Art, Music and Science (eds. R. Sarhangi and C. Sèguin), Tarquin Publications, Hertfordshire (2008), 311-318.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/106/

9. De Las Peñas, M.L.A.N. , Laigo, G. R. and Provido, E.B. Hyperbolic Semi-regular Tilings and their Symmetry Properties. Bridges Donostia: Mathematical Connections in Art, Music and Science (eds. R. Sarhangi and J.Barallo), Tarquin Publications, Hertfordshire (2007), 361-368.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/109/

10. Provido, E.B. and De Las Peñas, M.L.A.N. Determining Symmetry Groups of Semi-regular Tilings. Loyola Schools Review: Science & Engineering 6 (2007), 1-19.

11. An Approach in Coloring Semi-regular Tilings on the Hyperbolic Plane (with G. Laigo and R. Felix). Renaissance Banff: Mathematical Connections in Art, Music and Science (eds. R. Moody and R. Sarhangi), Central Plain Book Manufacturing Co, Winfield, Kansas (2005), 313-320.

link: https://archium.ateneo.edu/mathematics-faculty-pubs/111/

12. On Vertex Colorings of Archimedean Tilings with Applications in Molecular Symmetry (with A. Basilio). Loyola Schools Review; Science and Engineering 3 (2004), 125-137.