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A cone !
There are no triangular prisms in faces. Faces are 2-d shapes and these cannot contain 3-d shapes in them.
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A normal cone has a circular face as its base, and a slanting surface which goes from the circumference of this face to the vertex. So it has two faces. Mathematicians also refer to the infinite equivalent as a cone. This could be considered as a 3-d shape with one face.
None. A triangle is a 2-D figure, not a 3-D figure. Therefore, the concepts of faces and bases do not apply to it.