The lungs.
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Apex.
edges = 4 round base + 4 from vertices of base to apex = 8 edges corners = 4 round base + 1 apex = 5 vertices
It has a square base. Attached to each side of the base is a triangular face and these meet at an apex that is not in the plane of the square base. The apex need no be above the base: it can be to a side. The triangles can be scalene, acute, right or obtuse angled.
1/3 times the area of the base times the height from the center of the base to the apex.
A pyramid with a rectangular base coming up to an apex.