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Q: What is a solid figure with eight vertices and all of its faces are an equal size?

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A cube has eight vertices and six faces (think of a die!).

It is a cube or a cuboid that has 6 faces, 8 vertices and 12 edges

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A square-based pyramid.

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A hexagonal prism is a figure with hexagonal bases. A hexagonal prism has eight faces, eighteen edges, and twelve vertices.

A quadrilateral based pyramid.

A sphere- there are no faces, edges or vertices

According to the Euler characteristic, the number of faces, edges and vertices are related by: V - E + F = 2 for ANY convex polyhedron. If V = E then F = 2 faces. Also, E = F requires V = 2 vertices. No such figure exists.

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