# closedStar -- The closed star of a face of a complex.

## Synopsis

• Usage:
closedStar(F)
• Inputs:
• Outputs:
• ,

## Description

The closed star of the face F of the complex C.

 i1 : R=QQ[x_0..x_4] o1 = R o1 : PolynomialRing i2 : C=boundaryOfPolytope simplex(R) o2 = 3: x x x x x x x x x x x x x x x x x x x x 0 1 2 3 0 1 2 4 0 1 3 4 0 2 3 4 1 2 3 4 o2 : complex of dim 3 embedded in dim 4 (printing facets) equidimensional, simplicial, F-vector {1, 5, 10, 10, 5, 0}, Euler = -1 i3 : F=C.fc_0_0 o3 = x 0 o3 : face with 1 vertex i4 : link(F,C) o4 = 2: x x x x x x x x x x x x 1 2 3 1 2 4 1 3 4 2 3 4 o4 : complex of dim 2 embedded in dim 4 (printing facets) equidimensional, simplicial, F-vector {1, 4, 6, 4, 0, 0}, Euler = 1 i5 : closedStar(F,C) o5 = 3: x x x x x x x x x x x x x x x x 0 1 2 3 0 1 2 4 0 1 3 4 0 2 3 4 o5 : complex of dim 3 embedded in dim 4 (printing facets) equidimensional, simplicial, F-vector {1, 5, 10, 10, 4, 0}, Euler = 0 i6 : F=C.fc_1_0 o6 = x x 0 1 o6 : face with 2 vertices i7 : link(F,C) o7 = 1: x x x x x x 2 3 2 4 3 4 o7 : complex of dim 1 embedded in dim 4 (printing facets) equidimensional, simplicial, F-vector {1, 3, 3, 0, 0, 0}, Euler = -1 i8 : closedStar(F,C) o8 = 3: x x x x x x x x x x x x 0 1 2 3 0 1 2 4 0 1 3 4 o8 : complex of dim 3 embedded in dim 4 (printing facets) equidimensional, simplicial, F-vector {1, 5, 10, 9, 3, 0}, Euler = 0

 i9 : R=QQ[x_0..x_4] o9 = R o9 : PolynomialRing i10 : I=ideal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0) o10 = ideal (x x , x x , x x , x x , x x ) 0 1 1 2 2 3 3 4 0 4 o10 : Ideal of R i11 : C=idealToComplex I o11 = 1: x x x x x x x x x x 0 2 0 3 1 3 1 4 2 4 o11 : complex of dim 1 embedded in dim 4 (printing facets) equidimensional, simplicial, F-vector {1, 5, 5, 0, 0, 0}, Euler = -1 i12 : F=C.fc_0_0 o12 = x 0 o12 : face with 1 vertex i13 : link(F,C) o13 = 0: x x 2 3 o13 : complex of dim 0 embedded in dim 4 (printing facets) equidimensional, simplicial, F-vector {1, 2, 0, 0, 0, 0}, Euler = 1 i14 : closedStar(F,C) o14 = 1: x x x x 0 2 0 3 o14 : complex of dim 1 embedded in dim 4 (printing facets) equidimensional, simplicial, F-vector {1, 3, 2, 0, 0, 0}, Euler = 0 i15 : F=C.fc_1_0 o15 = x x 0 2 o15 : face with 2 vertices i16 : link(F,C) o16 = -1: {} o16 : complex of dim -1 embedded in dim 4 (printing facets) equidimensional, simplicial, F-vector {1, 0, 0, 0, 0, 0}, Euler = -1 i17 : closedStar(F,C) o17 = 1: x x 0 2 o17 : complex of dim 1 embedded in dim 4 (printing facets) equidimensional, simplicial, F-vector {1, 2, 1, 0, 0, 0}, Euler = 0

## See also

• link -- The link of a face of a complex.

## Ways to use closedStar :

• "closedStar(Face,Complex)"

## For the programmer

The object closedStar is .