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# AbstractSimplicialComplex _ ZZ -- the $k$ faces of a simplicial complex

- Operator: _
- Usage:
    `K_k`
- Inputs:
  - K, an abstract simplicial complex,
  - k, an integer,
- Outputs:
  - an abstract simplicial complex, the list of $k$ faces

## Description

This method returns the collection of $k$ faces of a given AbstractSimplicialComplex.

    i1 : K = abstractSimplicialComplex(3)

    o1 = AbstractSimplicialComplex{-1 => {{}}                   }
                                   0 => {{1}, {2}, {3}}
                                   1 => {{1, 2}, {1, 3}, {2, 3}}
                                   2 => {{1, 2, 3}}

    o1 : AbstractSimplicialComplex

    i2 : K_3

    o2 = {}

    o2 : List

    i3 : K_2

    o3 = {{1, 2, 3}}

    o3 : List

    i4 : K_1

    o4 = {{1, 2}, {1, 3}, {2, 3}}

    o4 : List

    i5 : K_0

    o5 = {{1}, {2}, {3}}

    o5 : List

    i6 : K_(-1)

    o6 = {{}}

    o6 : List

## Ways to use this method:

- AbstractSimplicialComplex _ ZZ -- the $k$ faces of a simplicial complex

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/AbstractSimplicialComplexes.m2:931:0.