0
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.
Add your answer:
Earn +20 pts
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
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 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.
Which polygons will tile the plane?
If it's interior angle is a factor of 360 then it will tessellate such as a square, a regular hexagon and an equilateral triangle.
Can you tile a surface with a regular hexagon?
Yes you can. Envision a beehive - it is made of regular hexagons.
Non-square rhombus polygons can tile the plane?
Yes.
