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It depends on the shape of the surface
Flat surface can be tiled by triangles, squares, and hexagons, these are the only combinations for the regular tessellations.
semi-regular tessellations (where multiple polygons are used in the same tiling)
There are in fact an infinite number of possible tessellations. All polygons can work from triangles to approaching a circle... a circle tiling would require an infinite number of infinitesimally small polygons around it, so you may or may not consider this a possibility.
NOT all polygons can be in the same tessellations, for example triangles, heptagons, and 42-gons cannot be in a 1:1:1 ratio.
In 3 dimensions regular polygons can be perfectly assembled into only 5 regular polyhedrons (3d version of polygon) (the platonic solids - these have been used to represent the elements, fire water, earth air and space)
tetrahedron consists of 4 triangles
cube (hexahedron) consists of 6 squares
octahedron 8 triangles
dodecahedron 12 pentagons
icosahedron 20 triangles
The hexagon didn't make it... possibly an infinite number of would assemble a sphere of infinite diameter, but this has never been included in any lists I've run across.
In 4 dimensions, there are six convex 4-polytopes, called (polychorons), the smallest of which is called the pentatope, and is composes of 10 triangles, which can only be done in 4 dimensions, it can't be constructed under normal circumstances in our worlds.
In 5, 6, 7, 8, 9, and 10 dimensions that are only 3 regular n-polytopes for each respectively... this may continue indefinitely but I don't know how to prove this, it's probably been done. If it does continue toward infinite dimensions that 2 and 3 dimensions are "special" and perhaps that is why we find ourselves in such a universe.
What else can I help you with?
Non-square rhombus polygons can tile the plane?
Yes.
Will a hexagon tile tessellate?
A regular hexagon will tessellate.
What is the surface area of a piece of tile that measures 11 x 14 centimeters?
43.543
Its possible to create a regular tessellation with a regular octagon?
No - because they would leave a small, square-shaped space between each tile.
What is the perimeter of tile?
If it is a square tile, then 4*side If it is a rectangular tile, then 2*(length + Width)
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 regular polygons can not tile a surface?
Regular polygons with 5, 7 or more sides.
Which regular polygons will fit together to tile a flat surface?
Triangles, squares and hexagons. That is if they all have to be the same. If you use different regular polygons, you can tile a flat surface with triangles and 12-sides or with squares and 8-sides for example.
What regular polygons can not be use to tile a floor by itself?
Bone
Can copies of a polygon be used to tile a surface?
Yes, copies of a polygon can be used to tile a surface, provided the polygon is a suitable shape. Regular polygons, like squares and equilateral triangles, can easily tile a plane without gaps or overlaps. However, some irregular polygons can also tile surfaces, depending on their angles and side lengths. The key requirement for a polygon to tile a surface is that it can cover the area without leaving any spaces between the tiles.
What are all the regular polygons that tile?
The only ones are equilateral triangles, squares and regular hexagons.
Is it possible to tile a floor with copies of a regular polygon?
Yes, but only with some polygons.
Will a regular polygon tile?
There are only three regular polygons which with tile. These a re a triangle, quadrilateral (square) and hexagon.This is because if there are n tiles meeting at a point, then the sum of the angles around that point must be 360 degrees - otherwise the polygons will overlap. The only regular polygons with interior angles that are factors of 360 are the ones mentioned above.
Can a regular pentagon and regular hexagon tile together in a plane?
Yes it can tile. * * * * * No, they cannot.
Can regular pentagons and regular hexagons tile a flat surface?
Regular pentagons cannot tile a flat surface without leaving gaps, as their internal angles (108 degrees) do not allow for a perfect fit. In contrast, regular hexagons can tile a flat surface efficiently because their internal angles (120 degrees) allow them to fit together perfectly without any gaps. Thus, while hexagons are capable of tiling, pentagons are not.
Can a octagon tile a flat surface alone?
A regular octagon cannot tile a flat surface, it needs squares as fillers. An irregular octagon can tile a flat surface alone.
Can squares and regular octagons tile a flat surface?
Yes, squares can tile a flat surface because their equal sides and right angles allow them to fit together without any gaps. Regular octagons, however, cannot tile a flat surface by themselves because their angles (135 degrees) do not allow for a perfect fit without leaving gaps. However, a combination of squares and octagons can tile a flat surface, as the squares can fill in the gaps created by the octagons. This arrangement is known as a semi-regular tiling.
