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Each angle in an equilateral triangle is 60 degrees. In order to create a regular tessellation of an area, we need for the angles of the polygons we are putting near each other to sum to 360 degrees. If you place six equilateral triangles so that all of them share a vertex, and each triangle is adjacent to two others, you get 60*6 = 360 degrees in that vertex. Please see related link for a demo of a triangular tessellation.
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Which regular polygon will tessellate alone?
An equilateral triangle, a square and a hexagon.
Will a regular isosceles triangle tessellate?
No, a regular isosceles triangle will not tessellate. In order for a shape to tessellate, it must be able to fit together with copies of itself without any gaps or overlaps. Regular isosceles triangles have angles of 90, 45, and 45 degrees, which do not allow for a repeating pattern that covers a plane without any spaces. Regular polygons that tessellate include equilateral triangles, squares, and hexagons.
Can all regular polygons tessellate?
No only three can tesselate. they are: An equilateral triangle, a square and a 6 sided hexagon.
Will a triangle tessellate?
No, a triangle will not tessellate by itself. In order for a shape to tessellate, it must be able to fit together with copies of itself without any gaps or overlaps. Triangles have angles that add up to 180 degrees, which does not allow them to fit together seamlessly to create a tessellation. Shapes like squares, hexagons, and equilateral triangles can tessellate because their angles allow them to fit together perfectly.
What regular shapes tessellate?
Any where the angles of 3 or more of the shape that meet at a point can add up to 360°, namely an equilateral triangle, a square and a hexagon.
