Three.
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Three edges meet at each vertex.
The shape you are describing is a rectangular prism. A rectangular prism has 8 vertices, with each vertex connecting three edges. It also has 6 faces, with each pair of opposite faces being parallel to each other.
Each one of the five points.
There are 9 edges. It has three edges which are parallel to each other (along the length of the prism) AND it has three pairs of parallel edges - at the top and bottom of the prism.
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