If, putting up the block of cubes, we go to the left instead of the right, but in all other respects build up in the same way, we obtain a block which has a curious relation to the first block.
The ordinary block is shown over again in Diagram III. Diagram IV. is the new block. The new block is like a looking-glass image of the old block. It is just the same, but that left and right is reversed.
Also, if we take selections of blocks we get figures which are just reversed. Thus 1, 4, 7, 8, in Block III., means a figure turned to the right; in Block IV. a figure turned to the left.
Again, consider the two figures formed by selecting the cubes 1, 4, 7, 8, 17, from Diagrams III. and IV. respectively. We get two figures which are just like one another as arrangements, but which we cannot turn into one another by twisting.
Diagram III. is a block.
Diagram V.
Considered as arrangements in themselves, these figures and these blocks seem to be identical, for the relationships of cube to cube which are present in the one are all present in the other. But considered as shapes they are not identical. For they will not coincide.
The whole matter becomes much more clear if we consider the relationship between the individual cube used and the block which it forms.