N-dimensional Sequential Move Puzzle - Glossary

Glossary

• Vertex. A zero-dimensional point at which higher-dimension figures meet.
• Edge. A one-dimensional figure at which higher-dimension figures meet.
• Face. A two-dimensional figure at which (for objects of dimension greater than three) higher-dimension figures meet.
• Cell. A three-dimensional figure at which (for objects of dimension greater than four) higher-dimension figures meet.
• n-Polytope. A n-dimensional figure continuing as above. A specific geometric shape may replace polytope where this is appropriate, such as 4-cube to mean the tesseract.
• n-cell. A higher-dimension figure containing n cells.
• Piece. A single moveable part of the puzzle having the same dimensionality as the whole puzzle.
• Cubie. In the solving community this is the term generally used for a 'piece'.
• Sticker. The coloured labels on the puzzle which identify the state of the puzzle. For instance, the corner cubies of a Rubik cube are a single piece but each has three stickers. The stickers in higher-dimensional puzzles will have a dimensionality greater than two. For instance, in the 4-cube, the stickers are three-dimensional solids.

For comparison purposes, the data relating to the standard 33 Rubik cube is as follows;

Number of achievable combinations

There is some debate over whether the face-centre cubies should be counted as separate pieces as they cannot be moved relative to each other. A different number of pieces may be given in different sources. In this article the face-centre cubies are counted as this makes the arithmetical sequences more consistent and they can certainly be rotated, a solution of which requires algorithms. However, the cubie right in the middle is not counted because it has no visible stickers and hence requires no solution. Arithmetically we should have

But P is always one short of this (or the n-dimensional extension of this formula) in the figures given in this article because C (or the corresponding highest-dimension polytope, for higher dimensions) is not being counted.