"""
I assume that you mean Synergetics and not Coxeter:

The (W,X,Y,Z) coordinates of the A-module are: (0,0,0,0), (2/3,0,0,0), (1,0,1,0), (2,2,2,0) 
The (W,X,Y,Z) coordinates of the B-module are: (0,0,0,0), (2/3,0,0,0), (2,1,1,0), (2,0,2,0) 
The (W,X,Y,Z) coordinates of the MITE are: (0,0,0,0), (1,0,1,0), (2,1,0,1), (1,2,1,0)

-- Alan Michelson
http://groups.yahoo.com/group/synergeo/message/32447

Followup:
http://groups.yahoo.com/group/synergeo/message/32503
"""

from __future__ import division # still needed in Python 2.5

"""
The following two modules may be obtained from
the Oregon Curriculum Network official website:
http://www.4dsolutions.net/ocn/python/
"""

# chakovian coordinates (fuller.4d)
from coords import Qvector  

# wrapper for VPython xyz vector (coxeter.3d)
from stickworks import Vector, Edge, axes
from math import degrees

a = Vector(Qvector((1,0,0,0)).xyz)
b = Vector(Qvector((0,1,0,0)).xyz)
c = Vector(Qvector((0,0,1,0)).xyz)
d = Vector(Qvector((0,0,0,1)).xyz)

sb = Vector(Qvector((0,0,0,0)).xyz)
pt = Vector(Qvector((2/3,0,0,0)).xyz)
oa = Vector(Qvector((1,0,1,0)).xyz)
bg = Vector(Qvector((2,2,2,0)).xyz)

b0 = Vector(Qvector((2,1,1,0)).xyz)
b1 = Vector(Qvector((2,0,2,0)).xyz)

m0 = Vector(Qvector((2,1,0,1)).xyz)
m1 = Vector(Qvector((1,2,1,0)).xyz)

class Tetrahedron (object):

    def __init__(self, v0, v1, v2, v3):
        # all possible edges between four vertices
        self.vertices = dict(A=v0,B=v1,C=v2,D=v3)
        self.faces = ['ABC','ACD','ADB','BCD']
        self.edges = [Edge(v0,v1), Edge(v0,v2), Edge(v0,v3),
                      Edge(v1,v2), Edge(v1,v3), Edge(v2,v3)]

    def draw(self):
        # VPython display
        for e in self.edges:
            e.draw()

    def _getangle(self, angle):
        c0 = self.vertices[angle[0]]
        c1 = self.vertices[angle[1]]
        c2 = self.vertices[angle[2]]
        return degrees((c0-c1).diff_angle(c2-c1))
        
    def rep_angles(self):
        for face in self.faces:
            for i,j,k in [(0,1,2),(1,2,0),(2,0,1)]:
                theangle = face[i]+face[j]+face[k]
                print 'Angle %s = %s' % (theangle, self._getangle(theangle))
                                     
class Amodule (Tetrahedron) :
    """
    A Module
    """
    def __init__(self):
        super(Amodule, self).__init__(sb, pt, oa, bg)


class Bmodule (Tetrahedron) :
    """
    B Module
    """    
    def __init__(self):
        super(Bmodule, self).__init__(sb, pt, b0, b1)            


class Mite (Tetrahedron) :
    """
    MITE Module
    """    
    def __init__(self):
        super(Mite, self).__init__(sb, oa, m0, m1)
        
def test0():
    """
    Source in Synergetics:
    http://www.rwgrayprojects.com/synergetics/s09/figs/f86421.html
    http://www.rwgrayprojects.com/synergetics/s09/figs/f86422.html
    """

    # green axes, please
    Edge.color = (0,1,0)
    axes(2,2,2)

    # red A module
    Edge.color = (1,0,0)    
    amod = Amodule()
    print "A mod angles:"
    amod.rep_angles()
    amod.draw()

    # blue B module
    Edge.color = (0,0,1)
    bmod = Bmodule()
    print "B mod angles:"
    bmod.rep_angles()
    bmod.draw()

    # cyan Mite module
    Edge.color = (0,1,1)
    mite = Mite()
    print "Mite angles:"
    mite.rep_angles()    
    mite.draw()

def test1():
    # Purple tetrahedron
    Edge.color = (1,0,1)    
    tet = Tetrahedron(a,b,c,d)
    tet.draw()
    print "Regular tetrahedron:"
    tet.rep_angles()
    
if __name__ == '__main__':
    test0()
    test1()    

"""
K. Urner, PKL, Feb 17 2007
"""