There are many such shapes.
A tetrahedron, triangular dipyramid, triangular prism, icosahedron are some examples.
Tetrahedron
base
prism:)
It is a cone.
Cone
the cone.
The simplest such shape is PYRAMID.
A pyramid has 1 square base.
It's the bottom of a 3-D shape or solid. For example, a square-based prism. The square face would be the base. Here's another example, a triangluar-based pyramid. The triangle would be the base.
cone
duodecahedron is a 3D shape that has 20 triangles as it's base
tetrahedra (a pyramid with a triangular base)