what are some geometric shapes that will not tesselate?

Question

I am doing a geometry project, and in it we have to provide a list of geometric shapes that will not tesselate. To tesselate is to cover an entire plane by repeating one shape over and over without overlapping or leaving empty spaces. I already have that circles and pentagons will not tesselate, but i cant think of any more to put on my list.

Answer 1

According to Wikipedia, the only regular polygons that will tessellate are triangles, squares, and hexagons:

http://en.wikipedia.org/wiki/Tessellation

You can tessellate an octagon with a square, but not just octagons.

So I think the answer would just be any polygon except those three.

Answer 2

Try thinking of shapes you can tessellate, then every time you find one that won't, add that to your list. I suspect there are actually very few objects that can be tessellated. Any object that can be tessellated is probably just a transformation of a few basic shapes.

Can any polygon with an odd number of sides more than three be tessellated? There is a start for you.

Interesting question. God bless you.

Answer 3

Shapes That Do Not Tessellate

Answer 4

any shape whose angles don't even divide into 360

for instance, a pentagon. and anything with more sides than a hexagon (because a hexagon has angles of 120, the next highest angle that would divide evenly into 360 is 180, and no polygon can have an angle of 180)

Answer 5

Pentagons will tesselate- you just have to rotate them. Ovals won't, kites won't, and isoseles trapezoids won't.

Hope I helped!

Answer 6

huhuhuhuh she said tesselates.