# fullCyclicPolytope -- Cyclic polytope.

## Synopsis

• Usage:
fullCyclicPolytope(d,R)
• Inputs:
• Outputs:
• C, ,

## Description

Returns the full cyclic polytope of dimension d with vertices the variables of R. A coker grading is added to R via the vertices of the moment curve (if R already has a coker grading then a warning is displayed) and translated such that 0 lies in the interior of C.

 i1 : R=QQ[x_0..x_5] o1 = R o1 : PolynomialRing i2 : C=fullCyclicPolytope(3,R) o2 = 3: x x x x x x 0 1 2 3 4 5 o2 : complex of dim 3 embedded in dim 3 (printing facets) equidimensional, non-simplicial, F-vector {1, 6, 12, 8, 1}, Euler = 0

## Ways to use fullCyclicPolytope :

• "fullCyclicPolytope(ZZ,PolynomialRing)"
• "fullCyclicPolytope(ZZ,PolynomialRing,PolynomialRing)"

## For the programmer

The object fullCyclicPolytope is .