No. The numbers are not consistent with the requirements of the Euler characteristic.
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.
It has 7 faces, 10 vertices, and 15 edges
It has 7 faces, 15 edges and 10 vertices
For all polyhedra: vertices + faces = edges + 2 The given fact is: edges = vertices + 10 → vertices + faces = vertices + 10 + 2 → faces = 12
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.
A pentagonal pyramid.
No. The given numbers do not satisfy the Euler characteristic for a simply connected polyhedron.
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
A pentagonal based pyramid has 6 faces, ten edges and 6 vertices.