20 Triangles

If 5 colors are given and all colors must be different for each triangle, we have 5*4*3/3=20 pieces. You can construct a trapezium with these pieces but an uniformly colored border isn't possible, because we need triangles with two same colored edges at the corners with 60° angles.

Other figures are possible.

If you want to cover an icosahedron by hand, you should do this with a net for this solid, keeping touching edges in mind. Then you can place the pieces on the icosahedron.

For a combination of an octahedron and a deltahedron with 12 faces nets and finished constructions are also shown.

Other combinations are given as virtual objects, if you click the pictures.

A tetrahedron with 4 faces and
a deltahedron with 16 faces can be combined.		 Another couple of deltahedrons with 6 and 14 faces
is also possible.		 Three deltahedrons with 4, 10 and 6 faces.

24 Triangles

There are 24 triangles with 4 colors and no restriction. This is the classic set to construct many figures, sometimes even with uniformly colored borders. I used this set with printed pieces to show three convex polygons.

A combination of a tetrahedron and an icosahedron can also be covered with these pieces. You can see the nets of the solids and the finished solutions. I didn't like the gaps betwween the triangles and didn't produce more triangles of this kind.

As virtual objects we have six other combinations.

8 and 16 faces 10 and 14 faces 4 and 20 faces
4, 6 and 14 faces 6, 8 and 10 faces 4, 8 and 12 faces

40 Triangles

A complete set of triangles with 3 different edge colors out of 6 colors has 6*5*4/3=40 elements. Here are the pieces made from magnetic foil with three colored stickers attached.

I used these pieces to cover a hexagon with a same colored border.

Other polygons are also possible.

Many combinations of deltahedrons can be covered, too. For one combination of three deltahedrons the nets with the pieces are shown

These are the finished objects.

Other cobinations are given as virtual objects.

4, 10 ,12 and 14 faces 4, 16 and 20 faces
6, 14 and 20 faces 8, 12 and 20 faces
4, 6, 10 and 20 faces 4, 6, 14 and 16 faces
4, 6, 8,10 and 12 faces 4, 8, 12 and 16 faces
A set of triangles with 3 out of 5 possible colors has (5³+2*5)/3=45 pieces. This set cannot be used for constructions since the number of same colored edges of all pieces is odd (45/5=9). Discarding the pieces with same colored edges we get 40 pieces. With this set you can cover all combinations of deltahedrons, which are already listed for the last set. Click the pictures to rotate the scenes.

4, 10 ,12 and 14 faces 4, 16 and 20 faces
6, 14 and 20 faces 8, 12 and 20 faces
4, 6, 10 and 20 faces 4, 6, 14 and 16 faces
4, 6, 8,10 and 12 faces 4, 8, 12 and 16 faces

70 Triangles

Coloring the triangles with 3 different colors out of 7 colors we get 7*6*5/3=70 pieces. I combined each piece with its mirror piece getting the rhombs in the picture.

A large hexagon with center symmetry is possible to construct with these pieces.

To get a combination of covered deltahedrons I placed the pieces in kind of nets of the solids and checked the edges for matching colors.

Then the pieces could easily be placed on the faces of the deltahedrons.

Other combinations are also possible.

4, 6, 10, 14, 16 and 20 faces 4, 8, 10, 12, 16 and 20 faces
6, 8, 10, 12, 14 and 20 faces 8, 12, 14, 16 and 20 faces

76 Triangles

If six colors are available and repetions of colors are allowed, we have (6³+2*6)/3=76 pieces. With these pieces we can cover 2-dim figures like some convex polygons, which could even be covered with a same colored border.

Three sets of deltahedrons with a total of 76 faces are also possible.

4, 6, 8, 10, 12, 16 and 20 faces 4, 8, 10, 12, 14, 16 and 20 faces 6, 8, 12, 14, 16 and 20 faces

90 Triangles

All eight deltahedrons together have a total of 90 faces. Therefore I looked for a set of 90 triangles where we can place marks of different color at different positions. Given 5 colors and 2 possible positions we can get 5*2=10 different edges. If two edges of a triangle are equal and one edge is different from the two ones, we have 10*9 different one-sided pieces. This is a set to cover all deltahedrons. As usual you can click the picture to get different points of view.