grunbaumBallComplex(PolynomialRing) -- make a nonshellable 3-ball with 14 vertices and 29 facets

Synopsis

• Function: grunbaumBallComplex

• Usage:

  grunbaumBallComplex S

• Inputs:
  • S, a polynomial ring, that has at least 14 generators
• Outputs:
  • an abstract simplicial complex,

Description

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

i2 : Δ = grunbaumBallComplex S;

i3 : matrix {facets Δ}

o3 = | hlmn elmn gkmn fkmn ghmn efmn bhln beln ghjn fhjn bfhn befn agkm afkm
     ------------------------------------------------------------------------
     ghim egim aegm aefm aghj dfhj adhj bghi cegi bcgi abgh bdfh abdh aceg
     ------------------------------------------------------------------------
     abcg |

             1      29
o3 : Matrix S  <-- S

i4 : dim Δ

o4 = 3

i5 : fVector Δ

o5 = {1, 14, 54, 70, 29}

o5 : List

i6 : assert(dim Δ === 3 and isPure Δ)

i7 : assert(fVector Δ === {1,14,54,70,29})

See also

• Making an abstract simplicial complex -- information about the basic constructors
• rudinBallComplex -- make a nonshellable 3-ball with 14 vertices and 41 facets
• zieglerBallComplex -- make a nonshellable 3-ball with 10 vertices and 21 facets
• isPure(SimplicialComplex) -- whether the facets are equidimensional