Infinitely many. The smallest side of a triangle can have infinitely many possible lengths.
A set of polygons might have such shapes in it. Certainly the set of all polygons does. So does the set of all polygons with fewer than 5 sides. Many other examples could be given. I am avoiding the use of the word "group", because it has a technical meaning in modern algebra.
An infinite number of shapes.
Tessera can be any shape. Often they are assumed to be polygonal but that is not a requirement. To see tessellation based on other shapes see the set of "Symmetry" artwork by MC Escher.
A square, a rectangle and a rhombus are three examples.
You can make 12 different shapes (counting flips) with 5 squares set orthogonally (not diagonally). These are called pentominos.
To make six sets using rhombuses, trapezoids, triangles, and hexagons, you would need a total of six sets. Each set would consist of one of each shape - a rhombus, a trapezoid, a triangle, and a hexagon. Therefore, you would need 6 sets x 4 shapes per set = 24 shapes in total to make six sets using these shapes.
The complement of the triangle in the plane.
A vortex is a spinning or whirling mass of fluid: liquid or gas. Typical examples are a whirlpool or whirlwind or hurricane. These are extended shapes and do not have a single set of coordinates.
by using a pool triangle rack
In the most common form of bowling in the US, ten pins are set up in a triangle.
Yes, a right triangle has only one set of perpendicular lines.
There is only one set of perpendicular lines in a right triangle; the horizontal line and the vertical line that make it 90 degrees.