What shape has 9 faces 9 vertices 16 edges?

Answer 1

All shapes that are 3-dimensional and closed are called polyhedrons. Polyhedron in greek decomposes into 'many faces.' The naming convention is to append -'hedron' to a greek prefix denoting the number of faces. Therefore any shape with nine faces will be a nonahedron.

In order to factor in the faces and edges systematically would require graph theory, because they depend on what shape each of the faces is and the organization of the arrangement.

Assuming:

1. you don't want to learn graph theory, and
2. the polyhedron has a realitively simple geometry

Google can help. Googling 'nonahedron' yields, among others, a polyhedron called an elongated square pyramid, which can be constructed by placing a square pyramid atop a cube (think of a house, where the roof comes to a single point). The square pyramid has 5 sides, the cube has 6, however one of each is removed when they are joined so the shape is a nonahedron(5+6-2=9). Similarly, the square pyramid has 5 vertices/8 edges and the cube has 8 vertices/12 edges with 4 edges/4 vertices shared; therefore the composite shape has 9 vertices (5+8-4=9) and 16 edges (12+8-4=16).

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All that is very interesting but avoids giving the simple answer which is an octagon based pyramid.

Answer 2

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