WebPolyiamonds are plane geometric figures constructed by pasting together equilateral triangles edge-to-edge. It is shown that a diophantine equation involving vertices of … WebJul 11, 2004 · Polyiamonds, which are animals residing on the triangular lattice, have been the subject of a few studies in recent years. For instance, in one of the first rigorous work …
Polyiamond - Wikipedia
WebJul 1, 2024 · A polyomino of size n is an edge-connected set of n cells on the square lattice \(\mathbb {Z}^2\).Similarly, a polyiamond of size n is an edge-connected set of n cells on … WebMar 24, 2024 · A generalization of the polyominoes using a collection of equal-sized equilateral triangles (instead of squares) arranged with coincident sides. Polyiamonds are … crypto as security
Polyomino, polyhex and polyiamond tiling
A polyiamond (also polyamond or simply iamond, or sometimes triangular polyomino ) is a polyform whose base form is an equilateral triangle. The word polyiamond is a back-formation from diamond, because this word is often used to describe the shape of a pair of equilateral triangles placed base to base, and the … See more The basic combinatorial question is, How many different polyiamonds exist with a given number of cells? Like polyominoes, polyiamonds may be either free or one-sided. Free polyiamonds are invariant under reflection as … See more Like polyominoes, but unlike polyhexes, polyiamonds have three-dimensional counterparts, formed by aggregating tetrahedra. However, polytetrahedra do not tile 3-space in the way polyiamonds can tile 2-space. See more Every polyiamond corresponds to a polyhex, as illustrated at right. Conversely, every polyhex is also a polyiamond, because each hexagonal cell of a polyhex is the union of six adjacent equilateral triangles. (Note, however, that neither correspondence is … See more • Triangular tiling • Rhombille tiling • Sphinx tiling See more Possible symmetries are mirror symmetry, 2-, 3-, and 6-fold rotational symmetry, and each combined with mirror symmetry. 2-fold rotational symmetry with and without mirror symmetry requires at least 2 and 4 triangles, respectively. 6-fold rotational symmetry … See more Every polyiamond of order 8 or less tiles the plane, except for the V-heptiamond. See more The set of 22 polyiamonds, from order 1 up to order 6, constitutes the shape of the playing pieces in the board game Blokus Trigon, where players attempt to tile a plane with as many … See more WebFeb 24, 2015 · Polyiamonds are polyforms constructed from unit equilateral triangles joined edge-to-edge on a triangular grid. The name comes from diamonds the same way … crypto as property