Pyramid
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A cuboid, a parallelepiped.
Yes. I think of an edge as a line. The edges meet at vertices, and the faces meet at edges.
A sphere. A sphere is a solid figure that has no faces, edges, or vertices. This is because it is completely round; it has no flat sides or corners.
Well, honey, I hate to break it to you, but that solid you're talking about is a triangular prism. It's got 17 faces, 15 edges, and 10 vertices. So, there you have it - a triangular prism strutting its stuff with all those faces, edges, and vertices.
triangular pyramid