How to properly draw hexagons with offset coordinates?

Question

This is my code:

import matplotlib.pyplot as plt
from matplotlib.patches import RegularPolygon
import numpy as np


offCoord = [[-2,-2],[-1,-2],[0,-2],[1,-2],[2,-2]]

fig, ax = plt.subplots(1)
ax.set_aspect('equal')

for c in offCoord:
    hex = RegularPolygon((c[0], c[1]), numVertices=6, radius=2./3., alpha=0.2, edgecolor='k')
    ax.add_patch(hex)
plt.autoscale(enable = True)
plt.show()

Expected result vs actual result in the attached image

Please tell me why my hexagons are not lined up edge by edge but overlap each other? What am I doing wrong?

Answer 1

Use law of cosines (for isosceles triangle with angle 120 degrees and sides r, r, and 1):

1 = r*r + r*r - 2*r*r*cos(2pi/3) = r*r + r*r + r*r = 3*r*r

r = sqrt(1/3)

This is the right code:

import matplotlib.pyplot as plt
from matplotlib.patches import RegularPolygon
import numpy as np


offCoord = [[-2,-2],[-1,-2],[0,-2],[1,-2],[2,-2]]

fig, ax = plt.subplots(1)
ax.set_aspect('equal')

for c in offCoord:
    # fix radius here
    hexagon = RegularPolygon((c[0], c[1]), numVertices=6, radius=np.sqrt(1/3), alpha=0.2, edgecolor='k')
    ax.add_patch(hexagon)
plt.autoscale(enable = True)
plt.show()