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I've successfully used FindGeometricTransformation to project the simplex triangle onto the x-y plane:

{error, xf} = 
  FindGeometricTransform[
     {{0, 0, 0}, {1, 0, 0}, {1, Tan[Pi/3], 0}/2}, 
     {{0, 0, 1}, {1, 0, 0}, {0, 1, 0}}];

When I try a simple extension of this to one higher dimension, it fails to compute the transformation.

{error, xf} = 
  FindGeometricTransform[
     {{0, 0, 0, 0}, {1, 0, 0, 0}, {1, Tan[Pi/3], 0, 0}/2, {1/2, Tan[Pi/3]/4, Sqrt[2/3], 0}}, 
     {{0, 0, 1, 0}, {1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 0, 1}}];

I get the error "FindGeometricTransform::insufficientPts: Need at least 2 non-degenerate pairs of points for Automatic transformation estimation." Any advice?

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  • $\begingroup$ This error message is not documented anywhere in the help. So only suggestion is to contact support@wolfram.com, someone with access to the source code internally will be able to know. It could be simply that it does not support larger than 3 dimensions space. $\endgroup$ – Nasser Jul 4 '14 at 9:26
  • $\begingroup$ You're right, @Nasser, after looking more carefully at the examples in link, I think it is limited to 3D. It was easy enough to come up with a transformation matrix in my case. $\endgroup$ – Hanmyo Jul 6 '14 at 11:52

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