dim C
Given a cell C, dim returns its dimension. In general the dimension of the cell is inferred from the dimension of its boundary. However, this can be overridden if the cell is created using newCell with the CellDimension option.
i1 : R = QQ[x,y,z];
i2 : vx = newSimplexCell({},x);
i3 : vy = newSimplexCell({},y);
i4 : vz = newSimplexCell({},z);
i5 : exy = newSimplexCell {vx,vy};
i6 : C = cellComplex(R,{exy,vz});
i7 : dim(vz) o7 = 0
i8 : dim(exy) o8 = 1