How to calculate vertices of dodecahedron using W|A?

Can I calculate for example with wolfram alpha coordinates of vertices of dodecahedron? I know coordinates of center point of dodecahedron (center of gravity) and the height of dodecahedron.

Yes, Wolfram Alpha can do it. Inputting PolyhedronData["Dodecahedron", "VertexCoordinates"] into Wolfram Alpha will yield a set of vertex coordinates you can use for a dodecahedron with unit edge length. Alternatively, MathWorld gives a simple set of coordinates for a dodecahedron with edge length $\dfrac2{\phi}$, where $\phi$ is the golden ratio: $(0,\pm\phi^{-1},\pm\phi),(\pm\phi^{-1},\pm\phi,0),(\pm\phi,0,\pm\phi^{-1}),(\pm 1,\pm 1,\pm 1)$ and all combinations of signs are taken.