Geodesic
Fundamental domains for rhombic lattices with dihedral symmetry of order 8
Joseph Ray Clarence G. Damasco1 ; Dirk Frettlöh2 ; Manuel Joseph C. Loquias1
1Institute of Mathematics, University of the Philippines Diliman
2Technische Fakultät, Universität Bielefeld
The electronic journal of combinatorics, Tome 26 (2019) no. 3
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We show by construction that every rhombic lattice $\Gamma$ in $\mathbb{R}^{2}$ has a fundamental domain whose symmetry group contains the point group of $\Gamma$ as a subgroup of index $2$. This solves the last open case of a question raised in a preprint by the authors on fundamental domains for planar lattices whose symmetry groups properly contain the point groups of the lattices.
DOI : 10.37236/7802
Classification : 52C05, 05B45, 52C20
Mots-clés : plane lattice, point group, fundamental domain, symmetry group

Joseph Ray Clarence G. Damasco  1   ; Dirk Frettlöh  2   ; Manuel Joseph C. Loquias  1

1 Institute of Mathematics, University of the Philippines Diliman
2 Technische Fakultät, Universität Bielefeld 
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     author = {Joseph Ray Clarence G. Damasco and Dirk Frettl\"oh and Manuel Joseph C. Loquias},
     title = {Fundamental domains for rhombic lattices with dihedral symmetry of order 8},
     journal = {The electronic journal of combinatorics},
     year = {2019},
     volume = {26},
     number = {3},
     doi = {10.37236/7802},
     zbl = {1423.52034},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/7802/}
}
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Joseph Ray Clarence G. Damasco; Dirk Frettlöh; Manuel Joseph C. Loquias. Fundamental domains for rhombic lattices with dihedral symmetry of order 8. The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/7802

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