Yes, it is true that you cannot tessellate seven-sided regular polygons (heptagons) by themselves. This is because the interior angle of a regular heptagon is approximately 128.57 degrees, which does not divide evenly into 360 degrees. As a result, heptagons cannot fit together without leaving gaps or overlapping, thus preventing them from tessellating.
True
Mostly true - you cannot tessellate only regular pentagons in two dimensions, since you cannot sum up the intersection of the angles to 360 degrees. If you tessellate a regular pentagon in three dimensions, you end up with a dodecahedron.
In the Euclidean plane, only three types of regular polygons can tessellate: equilateral triangles, squares, and regular hexagons. This is because their interior angles can perfectly add up to 360 degrees at each vertex. Other regular polygons, such as pentagons or octagons, do not meet this criterion and thus cannot tessellate the plane.
Certain polygons, yes. Squares, Triangles and Hexagons are all shapes which, in their regular form, can tessellate. Other polygons cannot.
The only regular polygons which will tessellate are those with 3, 4 or 6 sides. But all irregular triangles, all irregular quadrilaterals, 15 classes of irregular convex pentagons and 3 classes of irregular convex hexagons will tessellate. In addition, there are concave polygons with different numbers of sides which will also tessellate.
five-sided polygons cannot tessellate
True
False
true
You cannot tessellate convex polygons with 7 or more sides.
Mostly true - you cannot tessellate only regular pentagons in two dimensions, since you cannot sum up the intersection of the angles to 360 degrees. If you tessellate a regular pentagon in three dimensions, you end up with a dodecahedron.
True.
True
A regular octagon will not tessellate - the 'spaces' left over are squares.
Most regular polygons will not tessellate but if their interior angles is a factor of 360 degrees then they will tessellate or if their angles around a point add up to 360 degrees then they also will tessellate.
Some can, but not all. For example, rhombi, rhomboids, oblongs, and isosceles triangles can tessellate; however, most irregular polygons cannot. * * * * * True, but an incomplete answer. All triangles and quadrilaterals, whether regular or irregular, will tessellate. No regular pentagon will tessellate but (as of 2016), there are 15 irregular pentagons which will tessellate. There are 3 convex hexagons, (regular and 2 irregular) which will tessellate. No polygon with 7 or more sides, even if it is regular, will tessellate.
Certain polygons, yes. Squares, Triangles and Hexagons are all shapes which, in their regular form, can tessellate. Other polygons cannot.