There are several polyhedra with 8 vertices. Some examples are:
A heptagonal pyramid
A hexagonal prism
A hexagonal dipyramid (two hexagonal pyramid stuck together along their hexagonal bases)
There is also the 2-dimensional polygon - the octagon.
2 solid shapes together have 8 faces, 12 edges 8 vertices
A square or rectangle
octagon
A vertex is a corner where two sides meet. With flat shapes like triangles and octagons they are often called angles. An octagon has 8 vertices, and 8 sides.
A cube or a cuboid both have 8 corners which are known as vertices
The numbers do not satisfy Euler's characteristic so there can be no such polyhedron.
Rectangular pyramids
Pyramid
cube 8
For two dimensional shapes, a vertex (plural vertices) is a point where two sides meet.For 3D shapes, a vertex is a point where three or more faces meet.
In two dimensions, all sorts of triangles. In 3 or more dimensions there is no specific name for shapes with three vertices.
5 Shapes, 8 sides