That would be a regular octahedron. See http://en.wikipedia.org/wiki/Octahedron
Octahedron- A polyhedron with eight faces. All faces of a regular octahedron are congruent, equilateral triangles.
What polyhedron has eight sides and all of the are equilateral triangle?
Tetrahedron, icosahedron.
A regular octahedron.
If, by "sides" you mean faces, then the answer is a pentahedron.
Octohedron, or diamond
They are the faces of the polyhedron.
An octahedron
square pyramid
There is a contradiction in your question. If the base has four equal sides then is it a square so not all the faces are Triangles. However if the base is a square and the rest of the faces are triangles then your object is a "Square-based Pyramid"
an octagon
Tetrahedron, Hexahedron(cube), Octahedron, Dodecahedron, and Icosahedron