from pyx import canvas,path,color
from math import sqrt,tan,asin
 
pov = (-22.7,7.1,9.3)
x,y,z = 2,1,0
radius = 0.12
scale = 10.0
g = 2.0
h = 2.5

vertexColor = [color.rgb.red]
edgeColor = [color.rgb.black]
cubeColor = [color.rgb.blue]
 
def distance(p,q):
    return sqrt(sum([(p[i]-q[i])**2 for i in (x,y,z)]))
 
def perspective(loc):
    dz = loc[z]-pov[z]
    return (loc[x]-pov[x])*scale/dz, (loc[y]-pov[y])*scale/dz
 
def vertex(p):
    lx,ly = perspective(p)
    prad = scale*1.1*tan(asin(radius/(distance(p,pov))))
    c.fill(path.circle(lx,ly,prad),vertexColor)
 
def edge(p,q):
    lx1,ly1 = perspective(p)
    lx2,ly2 = perspective(q)
    c.stroke(path.line(lx1,ly1,lx2,ly2),edgeColor)

def cube(p,q):
    lx1,ly1 = perspective(p)
    lx2,ly2 = perspective(q)
    c.stroke(path.line(lx1,ly1,lx2,ly2),cubeColor)

c = canvas.canvas()

def transform(point,spin,flip,mirror,turn):
    x,y,z = point
    if mirror:
        x,y,z = y,x,z
    if turn:
        x,y,z = -x,-y,z
    if flip:
        x,y,z = -y,x,-z
    for i in range(spin):
        x,y,z = y,z,x
    return x,y,z

points = set()
lines = set()
for s in (0,1,2):
    for f in (0,1):
        points.add(transform((0,0,g),s,f,0,0))
        for m in (0,1):
            for t in (0,1):
                points.add(transform((g,g/h,g),s,f,m,t))
                points.add(transform((g*h,g,g),s,f,m,t))
            lines.add((transform((g*h,g,g),s,f,m,0),
                       transform((-g*h,-g,g),s,f,m,0)))

for a in (-2,2):
    for b in (-2,2):
        cube((a,b,-2),(a,b,2))
        cube((a,-2,b),(a,2,b))
        cube((-2,a,b),(2,a,b))

for p,q in lines:
   edge(p,q)
 
for p in points:
    vertex(p)
 
c.writePDFfile("Double_six")