That would be a square :D
A better name for "corners" would be angles, but the shape's name would be a hexagon
A general quadrilateral: it has no specific name.
There is, unfortunately, no special name.
the vertices are the corners to the shape, so you count the corners to whatever shape.
A parallelogram is a shape with opposite sides equal in length and parallel to each other. Examples of parallelograms are: rhombus, square, rectangle, and rhomboid.
A better name for "corners" would be angles, but the shape's name would be a hexagon
The hexagon has six corners and six sides.
A general quadrilateral: it has no specific name.
rhombus
There is, unfortunately, no special name.
Equilateral triangle.
a square
It could be an isosceles triangle, an isosceles trapezium, or miscellaneous polygons with no special name.
the vertices are the corners to the shape, so you count the corners to whatever shape.
Octogon. Eight sides, think of OCTOpus which has eight legs.
trapezoid
Not possible ! If the shape has four right-angles, at least two sides must be the same length.