The platonic solid built with 5 triangles to a vertex is an Icosahedron (20 faces). Here, the net is built from the original icosa, then "unfolding" occurs with each edge of the original icosa mapping to each edge of the 2D net with 20 triangles. 

As part of the Platonic Solids series, this model has clearly defined colors outlining the solid itself, scaffolding in black, and its dual in white.