Delian Brick

A Delian brick is a cuboid whose edge lengths are in the ratio

A plane perpendicular to its longest edges through their midpoints divides it into two congruent cuboids, each similar to the original. It is therefore a three-dimensional rep-2-tile, or rep-tile (Pegg 2018).

Let be the Delian constant. If the original edge lengths are 1, , and , then each half has edge lengths , 1, and in increasing order. Since , the similarity ratio of each half to the original is , and its volume is half that of the original.

Pegg (2018) used the name "Delian brick" for this self-similar cuboid. This attribution concerns the name rather than discovery of the solid.