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.
A tetrahedron is a four sided polyhedron. Each face is a triangle. If it is a regular tetrahedron, then each face is an equilateral triangle.
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.
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 need not have any verticals.