This polyhedron will be made from decagons and triangles. You will need 6 colors for the decagons and one color for the triangles.
To see the full-sized template click on this image:
You will need to prepare 12 of the faces with the decagon template. Make 2 decagons of each color. You will then need 20 same-colored triangle faces.
You can assemble this polyhedron by attaching 3 decagonal faces to one of the triangles. The 10 edges of each decagonal face will be glued alternately to a triangle and then to another decagonal face. All of the triangle faces will be surrounded by decagons.
Beginning at the bottom of the polyhedron, you should be able to add the next appropriate face according to the rule above ... surround each triangle with 3 decagons and alternate decagons and triangles around each decagon. Continue adding faces in this manner until your polyhedron has closed at the top.