Description
The star of a face $f$ in $D$ is the simplicial complex whose faces are the subsets $g$ with $f \cup g$ is a face of $D$.
The bow-tie complex.
i1 : R = QQ[x_1..x_5];
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i2 : bowtie = simplicialComplex {x_1*x_2*x_3,x_3*x_4*x_5}
o2 = | x_3x_4x_5 x_1x_2x_3 |
o2 : SimplicialComplex
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i3 : star(bowtie,x_3)
o3 = | x_3x_4x_5 x_1x_2x_3 |
o3 : SimplicialComplex
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i4 : star(bowtie,x_1*x_2)
o4 = | x_1x_2x_3 |
o4 : SimplicialComplex
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The 3-simplex and a copy of its boundary glued along a triangle.
i5 : R = QQ[a..e];
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i6 : D = simplicialComplex {a*b*c*d, b*c*e, b*d*e, c*d*e}
o6 = | cde bde bce abcd |
o6 : SimplicialComplex
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i7 : star(D,b*c*d)
o7 = | abcd |
o7 : SimplicialComplex
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i8 : star(D,b)
o8 = | bde bce abcd |
o8 : SimplicialComplex
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