false
No - because they would leave a small, square-shaped space between each tile.
Most regular polygons will not - by themselves. In fact, of the regular polygons, only a triangle, square and hexagon will. No other regular polygon will create a regular tessellation.
A heptagon has seven sides, so it will have seven lines of symmetry. Each line of symmetry will pass through a vertex and the midpoint of the opposite side. These lines divide the heptagon into mirror-image halves, making it symmetrical.
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.
A triangle has the fewest amount of sides possible to create a closed figure.
No, it is not possible to create a regular tessellation using regular heptagons. A regular tessellation requires that the interior angles of the shapes used add up perfectly around a point, and the interior angle of a regular heptagon is approximately 128.57 degrees. Since this angle does not divide evenly into 360 degrees, regular heptagons cannot tessellate the plane without leaving gaps or overlapping.
No it is not.
Each interior angle of a regular heptagon measures 900/7 degrees.The interior angles of all polygons meeting at a point must sum to 360 degrees. But that would require 360 / (900/7) = 2.8 - that is you would require 2.8 regular heptagons to meet at each vertex. Since it is not possible to have a fraction of a heptagon. the tessellation required by the question is impossible.
false
yes
Yes
Inly if the polygon has 3, 4 or 6 sides.
Assuming that the question refers to a regular octagon (not a regualr otagon), the answer is no.
No - because they would leave a small, square-shaped space between each tile.
Regular Hexagon, Square, and Equilateral Triangle. (Apex)
regular hexagon, square, equilateral triangle...apex
regular hexagon