The 3D shape that has 6 vertices, 6 faces, and 10 edges is a hexagonal prism. A hexagonal prism is a polyhedron with two hexagonal faces and six rectangular faces connecting them. It has 6 vertices where the edges meet, 6 faces (2 hexagonal and 4 rectangular), and 10 edges that form the boundaries between the faces.
A pentagonal pyramid has 6 faces, 6 vertices and 10 edges.
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
7 faces. 10 vertices. 15 edges.
The shape you are describing is a truncated octahedron. A truncated octahedron is a polyhedron with 16 vertices, 24 edges, and 10 faces. It is created by truncating an octahedron by cutting off its corners, resulting in a shape with hexagonal and square faces.
Such a polyhedron cannot exist. According to the Euler characteristics, V + F - E = 2, where V = vertices, F = faces, E = edges. This would require that the polyhedron had only two faces.
Oh, dude, it's like a math riddle! So, if a polyhedron has 10 more edges than vertices, we can use Euler's formula: Faces + Vertices - Edges = 2. Since we know the relationship between edges and vertices, we can substitute that in and solve for faces. So, it would have 22 faces. Math can be fun... sometimes.
A pentagonal pyramid.
No. The given numbers do not satisfy the Euler characteristic for a simply connected polyhedron.
The 3D shape that has 6 vertices, 6 faces, and 10 edges is a hexagonal prism. A hexagonal prism is a polyhedron with two hexagonal faces and six rectangular faces connecting them. It has 6 vertices where the edges meet, 6 faces (2 hexagonal and 4 rectangular), and 10 edges that form the boundaries between the faces.
Faces: 10 Vertices: 16 Edges: 24
Not any normal polyhedron since the numbers are contary to the Euler characteristic.
There can be no such polyhedron since the given numbers are not consistent with the Euler characteristic.
A pentagonal pyramid has 6 faces, 6 vertices and 10 edges.
A pentagonal pyramid has 6 faces, 6 vertices and 10 edges.
A pentagonal prism has 7 faces, 10 vertices and 15 edges.
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