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Q: Can a tiling be constructed entirely with equilateral triangles?
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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.