The smallest n-gons which can be assembled to a tetrad with no hole are hexagons (n = 6).
(The above holds if the conjecture that holeless pentagons cannot form a tetrad is true.)
What is the smallest possible number of vertices VT of a tetrad made of hexagon tiles?.
Polyomino tetrad with VT = 8

Suitable polyomino tiles have at least 6 edges and 6 vertices.
Although Scott Kim's polyomino tetrad has a hole, the number of vertices is very small.
Moreover the shape of the tetrad is mirror symmetric.

Polyiamond tetrad with VT = 8

Suitable polyiamond tiles have at least 6 edges and 6 vertices.
The marvelous tetrad of Scott Kim and Frank Rubin has only 8 vertices.
But also a polyiamond tetrad with a hole can have only 8 vertices.

 Open problem: Is there a tetrad which is a triangle and has a triangle hole (and no other holes)?

Polygon tetrads with VT = 9 and VT = 7

In Scientific American another mirror symmetric tetrad of Scott Kim was published. It has 9 vertices.

This tetrad can be modified. And we obtain a new record: VT = 7

In order to get a balanced shape we add the condition c = d.

 Open problem: Is there a holeless tetrad which is a hexagon?