# [Edu-sig] Tetrahedron class with volume computer based on edges only

kirby urner kirby.urner at gmail.com
Sun Aug 18 00:24:53 CEST 2013

```"""
Euler volume, modified by Gerald de Jong
"""
from math import sqrt, hypot

class Tetrahedron:
"""
Takes six edges of tetrahedron with faces
(a,b,d)(b,c,e)(c,a,f)(d,e,f) -- returns volume
if ivm and xyz
"""

def __init__(self, a,b,c,d,e,f):
self.a, self.a2 = a, a**2
self.b, self.b2 = b, b**2
self.c, self.c2 = c, c**2
self.d, self.d2 = d, d**2
self.e, self.e2 = e, e**2
self.f, self.f2 = f, f**2

def ivm_volume(self):
return round(ivmvol,5)

def xyz_volume(self):
ivmvol = sqrt(8/9) * self.ivm_volume()
return round(ivmvol,5)

a2,b2,c2,d2,e2,f2 = self.a2, self.b2, self.c2, self.d2, self.e2,
self.f2
sumval = f2*a2*b2
sumval +=  d2 * a2 * c2
sumval +=  a2 * b2 * e2
sumval +=  c2 * b2 * d2
sumval +=  e2 * c2 * a2
sumval +=  f2 * c2 * b2
sumval +=  e2 * d2 * a2
sumval +=  b2 * d2 * f2
sumval +=  b2 * e2 * f2
sumval +=  d2 * e2 * c2
sumval +=  a2 * f2 * e2
sumval +=  d2 * f2 * c2
return sumval

a2,b2,c2,d2,e2,f2 = self.a2, self.b2, self.c2, self.d2, self.e2,
self.f2
sumval =   a2 * b2 * d2
sumval +=  d2 * e2 * f2
sumval +=  b2 * c2 * e2
sumval +=  a2 * c2 * f2
return sumval

a2,b2,c2,d2,e2,f2 = self.a2, self.b2, self.c2, self.d2, self.e2,
self.f2
sumval =  a2 * e2 * (a2 + e2)
sumval += b2 * f2 * (b2 + f2)
sumval += c2 * d2 * (c2 + d2)
return sumval

PHI = sqrt(5)/2 + 0.5

R =0.5
D =1.0

import unittest
class Test_Tetrahedron(unittest.TestCase):

def test_unit_volume(self):
tet = Tetrahedron(D, D, D, D, D, D)
self.assertAlmostEqual(tet.ivm_volume(), 1.0, "Volume not 1")

def test_unit_volume(self):
tet = Tetrahedron(R, R, R, R, R, R)
self.assertAlmostEqual(tet.xyz_volume(), 0.11785, "Volume not 1")

def test_phi_edge_tetra(self):
tet = Tetrahedron(D, D, D, D, D, PHI)
self.assertAlmostEqual(tet.ivm_volume(), 0.70711)

def test_right_tetra(self):
e = hypot(sqrt(3)/2, sqrt(3)/2)  # right tetrahedron
tet = Tetrahedron(D, D, D, D, D, e)
self.assertAlmostEqual(tet.xyz_volume(), 1.0, "Volume not 1")

if __name__ == "__main__":
unittest.main()
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mail.python.org/pipermail/edu-sig/attachments/20130817/d0f1eb5d/attachment.html>
```