Fundamental Domains for Rhombic Lattices with Dihedral Symmetry of Order 8

  • Joseph Ray Clarence G. Damasco
  • Dirk Frettlöh
  • Manuel Joseph C. Loquias


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.


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