May be a pyramid.
A triangular based pyramid.
That could be a triangular pyramid.
A triangular prism does!
A tetrahedron (a pyramid with a triangular base).
tetrahedron aka triangular pyramid
Triangular prisim
A triangular pyramid. This is one where all the faces are triangles - a three-sided base, from which three triangular faces rise to a single point - the apex.
You can call it a "triangular prism" rather than "triangular based prism" ... saying a prism is "triangular" imply that the base is a triangle. There's no other name that I know of. A prism is just a 3d shape, so all you have to say is <type of shape> + prism to get the point across.
A tetrahedron or triangular pyramid.
A triangular prism
A triangular pyramid has 4 corners and 6 edges (and 4 faces).
A triangular prism or a triangular based pyramid