zieglerBallComplex(PolynomialRing) -- make a nonshellable 3-ball with 10 vertices and 21 facets

Synopsis

• Function: zieglerBallComplex

• Usage:

  zieglerBallComplex S

• Inputs:
  • S, a polynomial ring, that has at least 10 generators
• Outputs:
  • an abstract simplicial complex,

Description

i1 : S = ZZ/101[a..n];

i2 : Δ = zieglerBallComplex S;

i3 : matrix {facets Δ}

o3 = | bfgj bcgj befj abej abcj aehi adhi aefi abfi abdi cfgh degh cdgh bcfh
     ------------------------------------------------------------------------
     adeh bcdh bcfg adeg acdg abef abcd |

             1      21
o3 : Matrix S  <-- S

i4 : dim Δ

o4 = 3

i5 : fVector Δ

o5 = {1, 10, 38, 50, 21}

o5 : List

i6 : assert(dim Δ === 3 and isPure Δ)

i7 : assert(fVector Δ === {1,10,38,50,21})

See also

• Making an abstract simplicial complex -- information about the basic constructors
• rudinBallComplex -- make a nonshellable 3-ball with 14 vertices and 41 facets
• grunbaumBallComplex -- make a nonshellable 3-ball with 14 vertices and 29 facets
• isPure(SimplicialComplex) -- whether the facets are equidimensional