Yes. A heptagonal pyramid.
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The number of edges and vertices ina polyhedron will depend on the polyhedron one selects either to study, build or etc...
Using Euler's Polyhedron formula V+F-E=2, givenF=14 and E=24, we have V=12.The polyhedron has 12 vertices.This assumes a genus-0 polyhedron. An example would be the hexagonal antiprism, a polyhedron having two hexagonal faces and 12 triangular faces.
A square is not a polyhedron, it is a polygon. A cube is not a polygon, it is a polyhedron.A square has 4 edges and 4 vertexes. It has no faces because it is not a polyhedron. If you cut the corners off of a square, the new polygon has 8 edges and 8 vertexes.A cube has 6 faces, 12 edges, and 8 vertexes. If you cut the corners off of a cube, the new polyhedron has 14 faces, 36 edges, and 24 vertexes.
A polyhedron is in a subclass of geometric solids. The difference is that a polyhedron must have flat faces and straight edges.
Octagon if you're talking polygon but a rectangular pyramid has 8 edges.