Hexagon
A Hexagon
Yes, all quadrilaterals will tessellate.
Yes, any quadrilateral will tessellate.
No. Hexagons and squares will each tessellate by themselves but one can not make a tessellation out of hexagons and squares combined. However, if you add in a third shape, the triangle, one can make a tessellation.
Yes. For example, any triangle, including a scalene triangle, will tessellate.
Tessellation is covering a 2-d surface. Tessellation and making a 3-d shape are not compatible processes. 12 regular pentagons will form a dodecahedron.
No it does not tessellate you have to pentagons in order for it to tessellate. * * * * * It is not at all clear what "have to pentagons" has to do with this. No polygon with 7 or more sides will tessellate. Octagons will tessellate if mixed with squares but that is not "proper" tessellation since it involved more than one shape.
yes it can, it is quite easy to pick a non tessellate shape and pick another shape(tessellate or not) that when put together make a square and there you go.
All triangles will tessellate. All quadrilaterals will tessellate There are 15 classes of convex pentagons (the latest discovered in 2015) which will tessellate. Regular hexagons will tessellate. In addition, there are 3 classes of irregular convex hexagons which will tessellate. No convex polygon with 7 or more sides will tessellate.
Some do, some don't. For regular tessellation, you require the interior angles to be a factor of 360 degrees. An octagon will not tessellate. On the other hand a triangle, which does not have an even number of sides, will.
Only an equilateral triangle, square and a regular hexagon can be used to make regular tessellations but there are innumerable polygonal and non-polygonal shapes which will tessellate by themselves, and others which will tessellate along with other shapes.
Yes. Tessellated hexagons are the basis of many natural structures such as honeycombs.