# SimplicialComplexFactory VSΒΆ

alg_top.spad line 3428 [edit on github]

VS: AbelianGroup

Provides functions to construct various simplicial complexes.

- band: () -> FiniteSimplicialComplex VS
Generate a minimal triangulation of the surface of a cylinder without ends

- dunceHat: () -> FiniteSimplicialComplex VS
Generate a minimal triangulation of dunce hat.

- kleinBottle: () -> FiniteSimplicialComplex VS
generate a minimal triangulation of the surface of a Klein bottle.

- line: () -> FiniteSimplicialComplex VS
create a simplicial complex containing a line.

- moebiusBand: () -> FiniteSimplicialComplex VS
Generate a minimal triangulation of the surface of a Moebius band. A one sided surface with a single external boundary line.

- projectiveSpace: Integer -> FiniteSimplicialComplex VS
Generate a minimal triangulation of the surface of a projective plane. A one sided surface which cannot be embedded in 3D space without intersecting itself. There are no external boundaries, every edge connects two faces. (A punctured projective plane is equivalent to a Moebius band)

- sphereSolid: NonNegativeInteger -> FiniteSimplicialComplex VS
Generate a simplicial complex equivalent to a solid hyper-sphere. That is, a solid volume with no holes in it, so we use a single

`n`

-dimensional simplex.

- sphereSurface: NonNegativeInteger -> FiniteSimplicialComplex VS
Generate a simplicial complex equivalent to the surface of a hyper-sphere. That is, the surface of a volume with no holes in it, so we use a minimal triangulation of the faces of a single simplex.

- torusSurface: () -> FiniteSimplicialComplex VS
generate a minimal triangulation of the surface of a 3-dimensional torus.