Setup

from math import sqrt as SQ
from matplotlib.patches import Polygon as poly
import matplotlib.pyplot as plt

c1 = SQ(3)/2
c2 = SQ(33)/12
c3 = (3*SQ(11)+6)/12
c4 = SQ(11)/2

def drawDiamond(ax, fig, pts):

    d = poly([pts[0][0], pts[1][0], pts[2][0],
              pts[3][0], pts[0][0], pts[2][0]],
              ec = 'k',
              fc = '#00000000',
              ls =":",
              lw = 2.5)
    ax.add_patch(d)
    
    for p in pts :
        ax.scatter(p[0][0],
                   p[0][1],
                   c = p[1],
                   lw = 10,
                   zorder = 2)
        
def vertDiamond(pts) :
    
    fig = plt.figure(figsize = (6, 6))
    ax = fig.add_subplot(111, xlim = (-0.1, 2.1), ylim = (0.1, 2.1))

    #Remove axes and ticks.
    for side in ['bottom', 'left', 'top', 'right']:
        ax.spines[side].set_visible(False)
    ax.set_xticks([])
    ax.set_yticks([])
    
    drawDiamond(ax, fig, pts)
    
    fig.savefig("2023.04.14 Express1.png",
                bbox_inches = 'tight')  
    

def solution(pts1, pts2, n) :
    
    fig = plt.figure(figsize = (12, 12))
    ax = fig.add_subplot(111, xlim = (-0.1, 2.3), ylim = (0.1, 2.3))

    #Remove axes and ticks.
    for side in ['bottom', 'left', 'top', 'right']:
        ax.spines[side].set_visible(False)
    ax.set_xticks([])
    ax.set_yticks([])
    
    drawDiamond(ax, fig, pts1)
    drawDiamond(ax, fig, pts2)
    ax.plot((pts1[3][0][0], pts2[3][0][0]),
            (pts1[3][0][1], pts2[3][0][1]),
             c = 'k',
             ls =":",
             lw = 2.5,
             zorder = 1)
    
    fig.savefig("2023.04.14 Express" + str(n) + ".png",
                bbox_inches = 'tight')   

pts = [([0.5, 1], 'r'),
       ([1, 1+c1], 'g'),
       ([1.5, 1], 'b'),
       ([1, 1-c1], 'g')]
vertDiamond(pts)

def triangle() :
    
    fig = plt.figure(figsize = (8, 8))
    ax = fig.add_subplot(111, xlim = (-0.1, 2.3), ylim = (0.1, 2.3))

    #Remove axes and ticks.
    for side in ['bottom', 'left', 'top', 'right']:
        ax.spines[side].set_visible(False)
    ax.set_xticks([])
    ax.set_yticks([])
    
    d = poly([[1, 0.5+c4], [0.5, 0.5], 
              [1.5, 0.5], [1, 0.5+c4]],
             ec = 'k',
             fc = '#00000000',
             ls =":",
             lw = 2.5)
    ax.add_patch(d)
    
    variables = [("√3", (0.6, 1.3), 'k'), 
                 ("√3", (1.25, 1.3), 'k'), 
                 ("1", (.965, 0.4), 'k'),
                 ("α", (.965, 1.9), 'k')]
    
    for v in variables :
        plt.annotate(v[0], v[1], c = v[2], fontsize = 20)
    
    fig.savefig("2023.04.14 Express2.png",
                bbox_inches = 'tight') 
triangle()

pts1 = [([0.75-c2, c3+SQ(3)/12], 'r'),
        ([1, 0.5+c4], 'g'),
        ([0.75+c2, c3-SQ(3)/12], 'b'),
        ([0.5, 0.5], 'g')]
pts2 = [([1.25+c2, c3+SQ(3)/12], 'r'),
        ([1, 0.5+c4], 'g'),
        ([1.25-c2, c3-SQ(3)/12], 'b'),
        ([1.5, 0.5], 'g')]  

solution(pts1, pts2, 3)

pts2 = [([1.25+c2, c3+SQ(3)/12], 'b'),
        ([1, 0.5+c4], 'g'),
        ([1.25-c2, c3-SQ(3)/12], 'r'),
        ([1.5, 0.5], 'g')]  

solution(pts1, pts2, 4)

Rohan Lewis

2023.04.17