How to Find the Coordinates of an Icosahedron's Faces?

[BJRowlett]

Ive posted this on gamedev.net, and figured Id post here aswell.

What I am trying to figure out, is how to get the coordinates (X, Y, Z) of the faces of an Icosahedron, without having to manually enter all the data.

This wouldn't be as hard, but the data structure for the information is as follows:
GeodesicSphere::Faces::Vertex::Coordinates

An example of this is:
(GeoSphere.FaceIndex[0].A.X, GeoSphere.FaceIndex[0].A.Y, GeoSphere.FaceIndex[0].A.Z)
(GeoSphere.FaceIndex[0].B.X, GeoSphere.FaceIndex[0].B.Y, GeoSphere.FaceIndex[0].B.Z)
(GeoSphere.FaceIndex[0].C.X, GeoSphere.FaceIndex[0].C.Y, GeoSphere.FaceIndex[0].C.Z)
Which holds the X,Y,Z values of the all the vertices on the first Face.

With this, I will have to assign the values to multiple indices coordinates, because adjacent faces share vertices. And I haven't found an easy way to do so.

Also, finding a efficient way of sorting the faces, my idea was to select one node to be a 'north pole' and select any face, then work around the icosahedron, moving down a level, and repeating. This way, I can always use two of the vertices from the previous face, and just calculate the new one.

If you have any ideas that would work better, it would be greatly appreciated.


~BJRowlett

 

[Helios]

I do recall the latitude of the non-pole nodes are arctan( 1/2 )

 

[DrGreg]

You might like to look up Icosahedron - Cartesian coordinates on Wikipedia.