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Add peak and ridge to glossary.md
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blobinaticuber committed Sep 17, 2024
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Expand Up @@ -14,22 +14,22 @@ A 1-dimensional turning axis is not always well-defined for higher-dimensional p
### Polytope elements

For an $N$-dimensional polytope:
(Some of these terms are from [Polytope - Wikipedia](https://en.m.wikipedia.org/wiki/Polytope#Elements))

- **vertex** = rank 0, single point
- **edge** = rank 1, line connecting two vertices
- **face** = rank 2, polygon constructed from edges
- **cell** = rank 3, polyhedron constructed from faces
- ...
- **$n$-face** = rank $n$, polytope constructed from rank $n-1$ elements
- ...
- **$N$-face** = rank $N$, polytope constructed from rank $N-1$ elements
- **peak** = $N-3$ face
- **ridge** = $N-2$ face
- **facet** = rank $N-1$, polytope constructed from rank $N-2$ elements

In 4D, we prefer **facet** rather than **cell**. In simple terms: on most puzzles, a **facet** is the thing with a single color.

### Pieces

Some of these terms are from [Polytope - Wikipedia](https://en.m.wikipedia.org/wiki/Polytope#Elements).

Basic definitions for an $N$-dimensional hypercubic puzzle:

- **corner** = piece with $N$ colors (4 colors in 4D)
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