Yes.
For example if you have a decagon in which the top, bottom and the four sides on the left are as in a regular decagon, and if the four sides on the right make the shape concave. These decagons will "slot" into one another.
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Any polygon with external angles which are equal to a factor of 360 will tessellate. The only regular polygons which will tessellate are equilateral triangles, squares, and hexagons.
Equilateral triangles, squares, and hexagons.
Equilateral triangle, square and regular hexagon.
No. Equilateral heptagons (7 sided figures) do not tessellate the plane. Not if no other polygons are allowed. But if you allow a (non-equilateral) pentagon then you might be able to tessellate the plane!
Equilateral triangle, square and regular hexagon.