Yes; A Cylinder.
triangular prism
cylinder: 3 faces, 2 edges, no vertex
A cylinder has 2 parallel circular edges
# of faces + # of edges + # of vertecies + 2
They are called a Vertices and it is where 2 edges meet.
a cylinder
There is no shape that has only 2 edges and 2 faces.
According to Euler none; for all 3d shapes: Vertices + Faces = Edges + 2 ⇒ 12 + 8 = 19 + 2 ⇒ 20 = 21 So unless 20 does equal 21, no 3d shape has 8 faces, 19 edges and 12 vertices. Any 3d shape with 8 faces would be an octahedron.
There is no particular name.
perpendicular
sphere