Generating list of hexagonal coordinates

Question

I am gonna try to frame this in an understandable way but please let me know if further clarification is necessary. I am trying to create a list of hexagonal coordinates (each pt(x,y) represents a point on the edge of a hexagon) in a list form, where all the points, centers, and edges are split into separate lists. I know the following code is incorrect, like pseudocode but this is what I am trying to do:

import numpy
from itertools import product

ratio = numpy.sqrt(3)/2

N = 120
N_X = int(numpy.sqrt(N)/ratio)
N_Y = N//N_X

sites = list()   #creates list of all sites
esites = list()    #creates list of edge sites
csites = list()    #creates list of center sites

for site in product(range(0,N_X),range(0,N_Y),range(0,1)): 

    x,y,z = site            # initializes the x, y, z components of the site list
    for x in site[::2,:,:]: # loops over every other x site, all y and z
        x = ratio*x         # multiplies every other x by ratio to get hexagon
        sites.append(site)  # appends to the sites

    if site = x[1:2,::2] or x[::2] and y[1::2,::2] or y[::2]:    # loops over the positions of the edge sites and appends or if not appends to the center 
        esites.append(site)
    else:
        csites.append(site)

Again, I know this code is mere pseudo code so please no negative comments, and yes I have read the past comments on generating hexagonal grids. Any input on how to do something like this would be greatly appreciated. The output I am expecting is a list with size of all the positions, another with all the edges, and one with all the corners.

Note I have tried this with zip and the output format won’t work with my program even by transforming the zip into a list.