It is extremely difficult to determine.
All triangles and quadrilaterals will tessellate.
There are 15 classes of irregular convex pentagons which will tessellate.
Regular hexagons and three classes of irregular convex hexagons will tessellate.
In addition there are several examples of concave polygons, particularly those with an even number of sides, which will tessellate.
Finally, there are very many non-polygonal shapes, some derived from polygons, which will also tessellate. For examples of this last class of shapes, search the web for MC Escher's Symmetry artwork.
A circle!
answer
It is rep-tile if all the tiles used for the tessellation are congruent.
All shapes have to be polygons, because there is no shape that has 1 or 2 sides. A tessellation has to be a shape, so that it can be repeated. Its not going to be much of a tessellation if its a line.. lol.. that isn't a tessellation
equilateral triangle
Tessellation is using multiple copies of a shape, usually a polygon, to cover a plane without gaps or overlaps. Each copy of this single shape is a tessellating unit.
No a pentagon is a single polygonal shape, A tessellation is a scheme for covering a plane, without gaps of overlaps, using multiple copies of the same basic shape. These are usually polygons.
A regular tessellation is based on only one regular polygonal shape. A semi-regular tessellation is based on two or more regular polygons.
A tessellation is created when a shape is repeated over and over again covering a plane without any gaps or overlaps.
regular hexagon
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.
polygon. It can be a triangle, square or hexagon. Any other tessellation requires irregular polygons (sides of unequal lengths) or more than one shape.