This icosahedron has nine triangular pyramids pointing inwards on each face. The same shape can also be described as a truncated icosahedron whose each face has been replaced with a pentagonal or hexagonal pyramid bearing a triangular pyramid on each face. I used an atypical striped pattern for coloring.
In theory, one could direct all the small pyramids to the outside and this is the way I originally made this model. However, in practice this setup proved rather unstable as the whole relatively large and heavy model was supported only by the pyramids’ tips. The variant with pyramids pointing inwards has a much smoother face surface and continuous edges which support it better.
Images show the model from different angles as well as snapshots from the assembly process. I folded the first version (with pyramids pointing outside) while learning for one of my quantum mechanics exams during my studies. Modular origami was a good way to relax between periods of intensive learning. After I noticed that the model was not as nice as I had expected, I took it apart and reassembled the units into the version with pyramids pointing inwards you see here.