There are two types of tiles: the convex ("Veks") at left, above, and the concave ("Kays") at right. Notice how, unlike dominoes, they are not symmetrical. There are 25 Veks and 20 Kays of each "handedness" the mirror-image version of the ones in the picture are also included. That makes for a total of 90 tiles in the set.
The color pips are in five colors, and each tile is a different color pair, representing all the ways 5 colors can be paired. The Kays omit the tiles where both pips are the same color, accounting for their fewer numbers. See how the inside angles of the Kays will fit around the shallower angle of the Veks, and how all the unit edges of all tiles are the same length. So it should be easy to get them to fit together, if only the angles would work as easily! Ah, there's the challenge.