There are no other shapes that have only four flat faces except for a tetrahedron, although the faces thatmake up the tetrahedron can be triangles of various shapes and need not be all identical.
Four triangular faces.
There are points (vertices) lines (edges) and polygons (faces).
Sphere, cuboid, tetrahedron.
tetrahedron (triangle-based pyramid)
There can be no formula for a tetrahedron since you have not specified what aspect the formula is supposed to calculate. Furthermore, although they are all triangular pyramids, tetrahedra can be tall, needle-like shapes or almost flat shapes.
Pentagon (and in 3d: triangular prism and tetrahedron.)
In 2 dimensions, a quadrilateral. In 3 dimensions, a tetrahedron.
A tetrahedron (4 faces) and an icosahedron (20).
Just one: a tetrahedron or triangular pyramid.
A tetrahedron is the smallest possible polyhedron: a closed 3-d shape with polygonal faces. It has 4 triangular faces, 4 vertices and 6 edges.