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Can regular heptagons and equalateral triangle tile a flat surface?
Wiki User
∙ 9y ago
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.
Wiki User
∙ 9y ago
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An isometric triangle is a 3 dimensional triangle shown on a flat surface or in 2 dimensions.
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The Surface area of a triangle = 0.5*base*height The volume of a prism = area of its cross-section*length
To what do the internal angles of a triangle add?
In Euclidean geometry, 180. Other answers are possible, depending on the surface on which the triangle is drawn.
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It is a regular tessellation.
How many surfaces does an equalateral triangle?
An equilateral triangle has one surface.
Which regular polygons will not tile a surface?
An [equilateral] triangle, square and hexagon are the only regular polygons which, by themselves, will tile a surface.
What is a formula for surface area of triangle?
K, well there is no surface area of a triangle, because a triangle is a 2s figure. Surface area is for a 3d figure. To find the regular area of a triangle the formula is 1/2 of the base X the height :) gl :P
Is a surface area of a triangle figured from the same formula?
well there is no surface area of a triangle, because a triangle is a 2s figure. Surface area is for a 3d figure. To find the regular area of a triangle the formula is 1/2 of the base X the height :) gl :P
A regular tessellation can use four different regular polygons to cover a surface true or false?
I think it's only 3: triangle, square and hexagon.
How do you solve the Surface area of a regular pyramid?
There is no "regular pyramid". There are triangle pyramids, square pyramids, pentagon pyramids, etc. With the information given in your question, there is no way to answer.
Is it possble for a triangle to have a right angle and an obtuse angle?
Not a plane triangle. With a triangle on a convex surface (eg on the surface of a sphere), the answer is Yes.
What type triangle has a measure as 128?
A triangle on a concave surface.
Is triangle is a convex or nonconvex?
A triangle is normally nonconvex on a flat surface
What is the surface area of a regular pyramid with sides of 13?
It is not possible to answer the question without knowing if the pyramid is a triangle based, square based or other polygon based pyramid.
What is a isometric triangle?
An isometric triangle is a 3 dimensional triangle shown on a flat surface or in 2 dimensions.
Can the summation of the angles of a triangle be more than 180 degree?
Not if the triangle is in a plane. But the answer is YES for a traingle on a convex surface - such as the surface of the earth.
