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A decahedron is a polyhedron with 10 faces. There are several versions of a decahedron, but none of these are regular. By definition, they all have 10 faces.

There is the octagonal prism - with 24 edges and 16 vertices,

the square anti-prism, with 16 edges and 8 vertices,

the square cupola, with 20 edges and 12 vertices,

the pentagonal bi-pyramid, with 15 edges and 7 vertices and

the augmented pentagonal prism, with 19 edges and 11 vertices.

See, for example, http://en.wikipedia.org/wiki/Decahedron

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