PENTAGONAL prism
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It is a pentagonal based pyramid that has 6 vertices, 6 faces and 10 edges
A shape that has fewer than 8 faces and fewer than 10 edges is a triangular prism. A triangular prism has 5 faces (2 triangular faces and 3 rectangular faces) and 9 edges. It meets the criteria of having fewer than 8 faces and fewer than 10 edges.
A heptagonal prism gas 21 edges.
Heptagonal Prism
There is no simply connected 3-dimensional shape that meets these requirements.