Yes, it does.
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yes... this figure does tessellate
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.
A regular pentagon will not tessellate.
A regular hexagon will tessellate.
Yes, they can tessellate provided they are suitably matched.