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Can a tiling be constructed entirely with equilateral triangles?
Wiki User
∙ 13y ago
yes
Wiki User
∙ 13y ago
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How is symmetry related to tessellation?
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.
Another name for tessellation?
Tiling.
What is the first np-hard problem?
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.
Can a hexagon form a tiling pattern?
yes
Can you make a tiling pattern with circles?
no you can not because it is round
Can a tiling be constructed with triangles and regular pentagons?
yes
Why do triangles make a tiling?
Because they can tessellate
Can regular heptagons and equalateral triangle tile a flat surface?
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.
What are the five main of tessellation?
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.
What are the five main types of tessellations?
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.
How do you measure for tiling?
to measure tiling with a mesuring tape
What is the result of tiling?
The result of tiling is the covering of a roof
What is a name for a tiling pattern?
the name for a tiling pattern is a TPattern.
When was Reinhold Tiling born?
Reinhold Tiling was born in 1893.
When did Reinhold Tiling die?
Reinhold Tiling died in 1933.
When was Heinrich Sylvester Theodor Tiling born?
Heinrich Sylvester Theodor Tiling was born in 1818.
When did Heinrich Sylvester Theodor Tiling die?
Heinrich Sylvester Theodor Tiling died in 1871.
