How to plot an icosahedron projection?

Question

Is there a way to plot Tissot's indicatrices on an unfolded icosahedron projection? What I am doing is plotting the indicatrices in Plate Carree projection and then manually map the image to the unfolded icosahedron. I got the following but I think this is not how the indicatrices should look on the icosahedron. Each face (triangle) is formed via inverse gnomonic projection of the icosahedron. I was expecting the indicatrices to be equal area, conformal and equidistant.