That 3D shape is called triangular pyramid.
tetrahedron
The 3D shape that has 6 vertices, 6 faces, and 10 edges is a hexagonal prism. A hexagonal prism is a polyhedron with two hexagonal faces and six rectangular faces connecting them. It has 6 vertices where the edges meet, 6 faces (2 hexagonal and 4 rectangular), and 10 edges that form the boundaries between the faces.
Pentagonal Pyramid
the triangular pyramid
It is a triangular prism that has 6 vertices, 9 edges and 5 faces.
That 3D shape is called triangular pyramid.
Since it has 9 faces it is a nonahedron. Not sure how many of the thousands of nonahedrons have 6 vertices.
tetrahedron
A triangular prism.
The 3D shape that has 6 vertices, 6 faces, and 10 edges is a hexagonal prism. A hexagonal prism is a polyhedron with two hexagonal faces and six rectangular faces connecting them. It has 6 vertices where the edges meet, 6 faces (2 hexagonal and 4 rectangular), and 10 edges that form the boundaries between the faces.
Pentagonal Pyramid
It is a cuboid
Triangular prism
the triangular pyramid
A Triangular based Pyramid has 4 vertices, 6 edges and 4 faces.
It is an octahedron that is a 3D shape with 8 faces