Line intersection turtle script not working as it should

Question

I am creating a script that visualises (or is supposed to) the most amount of intersections given an amount of lines using turtle in python. For some reason, the part of the code that is supposed to highlight all of the crossovers only highlights a few of them. I have experimented with loops, however to no luck. I don't know if it's an issue with the code that grabs the coordinates of intersections or if my loop just wasn't formed properly but it just doesn't (completely) work. My code is below:

import turtle

def find_intersection( p0, p1, p2, p3 ) :
    s10_x = p1[0] - p0[0]
    s10_y = p1[1] - p0[1]
    s32_x = p3[0] - p2[0]
    s32_y = p3[1] - p2[1]

    denom = s10_x * s32_y - s32_x * s10_y

    if denom == 0 : return None # collinear
    
    denom_is_positive = denom > 0
    s02_x = p0[0] - p2[0]
    s02_y = p0[1] - p2[1]

    s_numer = s10_x * s02_y - s10_y * s02_x

    if (s_numer < 0) == denom_is_positive : return None # no collision

    t_numer = s32_x * s02_y - s32_y * s02_x

    if (t_numer < 0) == denom_is_positive : return None # no collision

    if (s_numer > denom) == denom_is_positive or (t_numer > denom) == denom_is_positive : return None # no collision
    
    # collision detected
    t = t_numer / denom
    intersection_point = [p0[0] + (t * s10_x), p0[1] + (t * s10_y)]
    return intersection_point

def max_crossovers(num):
    segment_points=[]
    t = turtle.Turtle()
    t.speed(0) # 1:slowest, 3:slow, 5:normal, 10:fast, 0:fastest
    t.width(2.5)
    count=0 # Keeps track of how many iterations of the loop have taken place.
    while count < num:
        t.left(360/(num)) # Turns the required angle
        t.forward(20*num)
        t.backward(40*num) # Gives leeway for lines to crossover
        pA=list(t.pos()) # obtain x,y for point A
        t.forward(60*num)
        pB=list(t.pos()) # obtain x,y for point B
        t.backward(30*num) # Prepares turtle in position for the next iteration
        segment_points.append([pA, pB])
        count+=1

    print(segment_points)

    # THIS PART ONWARDS NEEDS TO BE IN A LOOP

    t.goto(find_intersection(segment_points[0][0], segment_points[0][1], segment_points[0+1][0], segment_points[0+1][1])[0], find_intersection(segment_points[0][0], segment_points[0][1], segment_points[0+1][0], segment_points[0+1][1])[1]) # go to the position of an intersection
    
    t.pencolor("red") # begin process of drawing a circle
    t.penup()
    t.left(90)
    t.backward(10)
    t.right(90)
    t.pendown()
    t.circle(10)
    t.penup()
    t.left(90)
    t.forward(10)
    t.right(90)

    # UNTIL HERE

max_crossovers(5) # Input number of lines to give the program.

I have tried experimenting with loops and to no luck. Maybe the issue is that the function to detect intersections doesn't work properly otherwise I might just have implemented the loop incorrectly?