What is a possible way to tile the plane with a parallelogram with 60° and 120° angles?
I: four at a vertex
II: three or six at a vertex
A) I only
B) II only
C) both I and II
D) neither I nor II

Question

What is a possible way to tile the plane with a parallelogram with 60° and 120° angles? 
I: four at a vertex
II: three or six at a vertex
A) I only
B) II only
C) both I and II
D) neither I nor II

Quizplus · Accepted Answer

It is possible to tile the plane using parallelograms with 60° and 120° angles in both ways described in options I and II.

I: Four at a vertex can be achieved by placing two parallelograms with opposite angles together at a vertex, then adding another pair of parallelograms adjacent to them so that their long edges are parallel to the long edges of the first pair.

II: Three or six at a vertex can be achieved by placing three parallelograms with opposite angles together at a vertex so that their long edges intersect at 120 degrees, forming a hexagon. This hexagon can then be tiled with six parallelograms, and this pattern can be repeated infinitely in all directions to tile the plane.

What Is a Possible Way to Tile the Plane with a Parallelogram