**hypercube**or more precisely, a tesseract when imposed within 2D space.

The orange squares represent the faces of the internal cell, a cube in 3D space, and is defined by vertices A to H. The larger bolder letters, I to P are the vertices of the outer cell/cube.
The diagonal lines are the edges which link the inner to the outer forming the faces that configure the cells which interface to the inner and outer cells. Let each hypercell have a value which is the vertex sum of each of its enclosing faces (or three times the sum of its 8 vertices). |

**A**

__always be__

**1**. Find sets of values for A through P so that all the cells have the same value.

__Note:__while the on-line calculator may be useful, a spreadsheet should prove more valuable for those able to use one.