0
$\begingroup$

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.

Thanks for advice.

  • 0
    There is an extensive discussion on the building of a dodecahedron and its vertices at this http://math.stackexchange.com/questions/632936/cleverest-construction-of-a-dodecahedron-icosahedron/1566268#1566268 StackExchange site.2015-12-08

1 Answers 1

1

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.