Tesselation (or tiling) generally implies translational symmetry, because you can generally move one part of a tiling over another a specific distance away and get an exact match (ie the tesselation is periodic). A counterexample (possibly the only one) is Penrose tiling, which is non-periodic. There is certainly no need for a tesselating shape to have either bilateral or rotational symmetry: all triangles and all parallelograms (including squares and rectangles) will tessellate. I'm afraid this is a rather superficial answer to this very interesting question; a deeper one will have to come from someone with a knowledge of group theory.
Tiling.
You can use the bounded tiling problem. Given a problem in NP A, it has a turing machine M that recognizes its language. We construct tiles for the bounded tiling problem that will simulate a run of M. Given input x, we ask if there is a tiling of the plane and answer that will simulate a run of M on x. We answer true iff there is such a tiling.
yes
no you can not because it is round
yes
Because they can tessellate
Equilateral triangles can tile a plane, but regular heptagons cannot; nor can they tile the plan together. Where vertices meet (at a point on the plane) there is a complete turn of 360°. Each vertex of an equilateral triangle is 60°; 360° ÷ 60° = 6, a whole number of times, so a whole number of equilateral triangles can meet at a vertex of the tiling. Each vertex of a regular heptagon is 128 4/7°; 360° ÷ 128 4/7° = 2 4/5 which is not a whole number, so a whole number of regular heptagons cannot meet at a vertex of the tiling, so there will be gaps. With one regular heptagon there are 360° - 128 4/7° = 232 3/7°, but this cannot be divided by 60° a whole number of times, so one regular heptagon and some equilateral triangles cannot meet at a vertex of the tiling without gaps. With two regular heptagons there are 360° - 2 x 128 4/7° = 102 6/7°, but this cannot be divided by 60° a whole number of times, so two regular heptagons and some equilateral triangles cannot meet at a vertex of the tiling without gaps. With three or more regular heptagons, they will overlap when trying to place them on a plane around a point - leaving no space for any equilateral triangles.
Tessellations are interesting and make for an interesting piece of art. There main types are normal tiling, monohedral tiling, isohedral tiling, penrose tiling, and voronoi tiling.
Tessellations are interesting and make for an interesting piece of art. There main types are normal tiling, monohedral tiling, isohedral tiling, penrose tiling, and voronoi tiling.
to measure tiling with a mesuring tape
The result of tiling is the covering of a roof
the name for a tiling pattern is a TPattern.
Reinhold Tiling was born in 1893.
Reinhold Tiling died in 1933.
Heinrich Sylvester Theodor Tiling was born in 1818.
Heinrich Sylvester Theodor Tiling died in 1871.