Yes
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regular hexagon
No. Each interior angle of a regular pentagon is 108 degrees. In order for tessellation to be possible, the sum of the angles meeting at a point must be 360 degrees. That is to ensure that all the space around that point is covered. But 108 is not a factor of 360 so it is not possible.
You have to specifically give the problem with the dots, but it can form all equilateral triangles.. .. . .. . . .