def new_polygon(biggon, ratio):
    """
    Given a polygon (biggon), this function returns the coordinates of
    the smaller polygon whose corners split the edges of the biggon by
    the given ratio.
    """
    smallgon = []
    L = len(biggon)
    
    for i in range(L):
        new_vertex = (biggon[i][0] *ratio + biggon[(i+1)%L][0] *(1-ratio),
                      biggon[i][1] *ratio + biggon[(i+1)%L][1] *(1-ratio), )
        smallgon.append(new_vertex)
        
    return tuple(smallgon)