Everyone knows the Domino game from the childhood time. The classical form shows in its two fields dice pictures or empty space on the top. With two from seven pictures there are 28 different Domino tiles. If we cut a Domino diagonally, we get one Dom and one Ino.
This funny introduction serves just for the justification of the name Dom for the half Dominos. The Domino pictures are meaningless in the following. Doms and Inos are apparently equal, so we concentrate on Doms generating a whole family of puzzles.
The simplest one is the DiDom puzzle. All DiDoms consist of two 1:2:√5 triangles. This way we get 13 different tiles, where the tile K – the kite – plays a very special role ( see [Logelium] About Kites ). Forms without kite rings are impossible to fill with the DiDom tiles.
Because there are no kite rings possible with a single kite, we use a double set of DiDoms with 2 * 13 tiles. With this set a lot of symmertic forms with area 2 * 13 * 2 = 52 can be filled.
We will investigate more deeply the convex forms, which can be filled with DiDom tiles ( see [Logelium] Convex DiDom Forms ).
The tile constructed from three Doms are called TriDom. There are 88 different tiles, where 16 contain a kite. In [2] Zucca only 86 TriDoms are shown, which is incorrect. (One Figure is a duplicate and there a three more). The complexity of TriDoms is dramatically higher than of DiDoms. The solution of a DiDom form can be calculated in a few seconds, but a form with all TriDoms exceeds any computing capacity. Again the 16 kite tiles play a very special role.
Besides tiles constructed only of Doms there are many mixed designs. The historical Stomachion is addressed with a dedicated chapter (see [Logelium] Stomachion).
The Dom idea can be used in triangular grids too. I produced a set of tiles I named DiTroms composed of Troms which are four regular triangles diagonally cut. There are 13 grid conform DiTroms plus one kite. I had not seen these tiles before but had no time to try solving any form with this kind of puzzle yet. (see also [Logelium] Triangular Kite Pairs)
