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# fan(PolyhedralComplex) -- Take the fan over a polyhedral complex

- Function: fan
- Usage:
    `F = fan PC`
- Inputs:
  - PC, an instance of the type PolyhedralComplex,
- Outputs:
  - F, an instance of the type Fan,

## Description

The polyhedral complex is embedded at height one and the fan is taken over it.

    i1 : C = hypercube 2

    o1 = C

    o1 : Polyhedron

    i2 : F = faces(1,C)

    o2 = {({0, 2}, {}), ({1, 3}, {}), ({0, 1}, {}), ({2, 3}, {})}

    o2 : List

    i3 : V = vertices C

    o3 = | -1 1  -1 1 |
         | -1 -1 1  1 |

                  2       4
    o3 : Matrix QQ  <-- QQ

    i4 : L = linealitySpace C

    o4 = 0

                  2
    o4 : Matrix QQ  <-- 0

    i5 : PC = polyhedralComplex(V,L,F)

    o5 = PC

    o5 : PolyhedralComplex

    i6 : vertices PC

    o6 = | -1 1  -1 1 |
         | -1 -1 1  1 |

                  2       4
    o6 : Matrix QQ  <-- QQ

    i7 : maxPolyhedra PC

    o7 = {({0, 2}, {}), ({1, 3}, {}), ({0, 1}, {}), ({2, 3}, {})}

    o7 : List

    i8 : dim PC

    o8 = 1

## Ways to use this method:

- fan(PolyhedralComplex) -- Take the fan over a polyhedral complex

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Polyhedra/documentation/documentation.m2:658:0.