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A rectangular based pyramid has 5 faces, 8 edges and 5 vertices whch is the plural of vertex.
A rectangular prism has 6 vertices. A rectangular pyramid has 5 vertices. 6-5= 1 more vertex
There are five of them. One at each corner of the rectangular base, and the fifth at the apex where the triangular faces meet.
There are many such solids: A heptagonal pyramid A cuboid (or rectangular prism) A hexagonal dipyramid A pentagonal pyramid with a 2-vertex shape on the other side etc.
There are five faces on a rectangular pyramid.