6 citations · 27 across the 18 of their papers we have counts for
8 papers · 1 filter
Similarity Isometries of Point Packings
Jeanine Concepcion H. Arias, Manuel Joseph C. Loquias
A linear isometry of is called a similarity isometry of a lattice if there exists a positive real number such that is a subla…
Color groups of colorings of -planar modules
Manuel Joseph C. Loquias, Lilibeth D. Valdez, Ma. Lailani B. Walo
A submodule of a -module determines a coloring of the module where each coset of the submodule is associated to a unique color. Given a submodule coloring of a $\mathbb…
Coincidence indices of sublattices and coincidences of colorings
Manuel Joseph C. Loquias, Peter Zeiner
Even though a lattice and its sublattices have the same group of coincidence isometries, the coincidence index of a coincidence isometry with respect to a lattice and to a su…
Symmetries and color symmetries of a family of tilings with a singular point
Imogene F. Evidente, Rene P. Felix, Manuel Joseph C. Loquias
We obtain tilings with a singular point by applying conformal maps on regular tilings of the Euclidean plane, and determine its symmetries. The resulting tilings are then symmetric…
Coincidences of a shifted hexagonal lattice and the hexagonal packing
Jeanine Concepcion H. Arias, Evelyn D. Gabinete, Manuel Joseph C. Loquias
A geometric study of twin and grain boundaries in crystals and quasicrystals is achieved via coincidence site lattices (CSLs) and coincidence site modules (CSMs), respectively. Rec…
The coincidence problem for shifted lattices and crystallographic point packings
Manuel Joseph C. Loquias, Peter Zeiner
A coincidence site lattice is a sublattice formed by the intersection of a lattice in with the image of under a linear isometry. Such a linear isometry is re…
Colourings of lattices and coincidence site lattices
Manuel Joseph C. Loquias, Peter Zeiner
The relationship between the coincidence indices of a lattice and a sublattice of is examined via the colouring of that is obtained by assigning a unique co…
Coincidence isometries of a shifted square lattice
Manuel Joseph C. Loquias, Peter Zeiner
We consider the coincidence problem for the square lattice that is translated by an arbitrary vector. General results are obtained about the set of coincidence isometries and the c…