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The shape can't exist: if you imagine a square face in 2D you have 4 edges and 4 vertices. Adding a further vertex out of the plane (introducing a 3rd dimension) you MUST have 4 more edges to join the original 4 vertices to the novel vertex. This sums to 8 edges as a minimum.
This is of course assuming Euclidean geometry.

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Q: What 3d shape has 5 edges 5 vertices's and 1 square face?
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