---
tag: VBM8ZYTT2X
kind: concept
name: n-skeleton
msc: [57Q05, 55U10]
sources:
  - url: https://en.wikipedia.org/wiki/N-skeleton
same_as:
  wikidata: Q5154570
  wikipedia: N-skeleton
---

## Summary

The $n$-skeleton of a CW complex or of a simplicial complex is the part made of the cells or simplices of dimension at most $n$.
The skeleta form an increasing sequence of subcomplexes whose union is the whole complex.
Each one is built from the previous one by attaching $n$-dimensional cells.
Induction over the skeleta is the main technique for proving facts about CW complexes.
The $n$-skeleton already determines the homotopy groups of the complex below degree $n$.

## Explanations

### L1 human

Think of a cube built in stages.
First come its $8$ corners, the $0$-skeleton.
Then the $12$ edges are added, giving a wire frame, the $1$-skeleton.
Then the $6$ square faces are glued in, giving the hollow box, the $2$-skeleton.
Finally, filling in the solid gives the whole cube.