Heptiamond Constructions

A number of problems have been proposed for the heptiamonds. One of these is to produce a quintuplications of the pieces. This would require 25 heptiamonds and so one piece must be used twice.

Alternatively the second copy of the piece could be considered as a hole. This is possible for all pieces.

The hole can also have a number of other areas. These constructions are by Pieter Torbijn.

We can even have multiple similar holes. These constructions also by Pieter Torbijn.

Mike Reid has also produced a number of these similar hole problems. A few here are five-fold replicas of heptominoes.

Another method of pentuplication is shown in Miroslav Vicher's site under expanded heptiamonds.

With 24 pieces it might be possible to produce three, four or six congruent shapes with a full set. All of these are possible as shown in the following diagrams by Pieter Torbijn.

Another version of the three congruent shapes is shown below.

A number of other symmetrical multiple shapes are possible as shown below. The first three solutions are by Mike Reid.

Mike has also produced a number of constructions based similar themes.

We can also join 6 heptiamonds and then extend the construction to make a shape similar to the original but twice the size. This solution is by Pieter Torbijn.

We may also look for a figure with the maximum number of internal holes. The best known solution is with 25 holes.

One Sided Heptiamonds

If we consider mirror image pairs as distinct then there are 43 heptiamonds. No parallelogram can be formed with this set and only one trapezium. This is shown here (solution by Pieter Torbijn).

The next diagram shows a number of symmetric figures formed with the set as well as a number of solutions to the simultaneous double triplication and pentuplication of one of the pieces. It is likely that all the heptiamonds can be used as the pattern for this construction. The figure at the bottom right shows a solution to the problem of simultaneous triplication and sextuplication with a similar hole in each figure and the final construction is of simultaneous three triplications and a quadruplication of a piece..