Below is current source for ch.py, a module for exploring volume relationships starting with a "ground state" (a default) known as the concentric hierarchy of polyhedra.
The user begets various polyhedra from their class definitions, then resizes them at will, perhaps using the * operator in place of the scale method: >>> import ch >>> rt = ch.R_Triac() >>> rt.volume 7.5 >>> rt = rt * pow(2/3., 1/3.) DEBUG: a star is born: a new R_Triac >>> rt.volume 5.0000000000000009 >>> rt.edge 0.61771467052713269 >>> rt = ch.R_Triac() >>> rt.edge 0.70710678118654757 >>> rt.edge_name 'long face diagonal' The concentric hierarchy is formed from the five Platonics, a primitive set that is closed under the operation of "make my dual". When the duals combine, e.g. the tetrahedron with itself, you have the option to intersect the edges so as to form yet another polyhedron (not necessarily Platonic). Here's what you can do with the five Platonics in that regard (i.e. o + o.dual == something). tetrahedron + tetrahedron == cube octahedron + cube == rhombic dodecahedron icosahedron + pentagonal dodecahedron == rhombic triacontahedron There's some question as to how to scale these relative to one another, when defining a ground state. The tetrahedron, cube, octahedron and rhombic dodecahedron all have obvious volume relationships if you start in this way. Anyway, here's my puzzle: I'm using Python 2.6, but my call to Poly.__init__ within its subclasses would surely be more stylish where super() used instead. However, all my trials with super(), have so far resulted in errors. If you fix this and even provide a clear explanation as to how this fix works, you might become part of a famous inner circle. The concentric hierarchy is poised to take the world by storm, at least in NCTM circles. Here's a lesson plan I've been touting. http://www.bfi.org/our_programs/bfi_community/synergetics (follow link to NCTM web site) Kirby PS: all the dual combos are rhombohedra i.e. have rhombic faces. You may criss-cross these diamond faces to get tri-rectangular tetrahedral wedge shapes that include the center point. In the case of the cube and rhombic dodecahedron, one gets the same shape, called a Mite in this namespace (for "minimum tetrahedron" -- it's a space-filler). In the case of the rhombic triacontahedron, one gets the T-module (T for triacontahedron). Provided our scaling is done right, 3 * T = Mite (volumetrically speaking). I will be adding these in a next edition. My thanks to David Koski for technical assistance on this project. *====== ch.py ====== from math import sqrt as radical phi = (1 + radical(5))/2 class Poly: def __init__(self, edge = 1, edge_name = "edge", volume = 1, greekname = "Tetrahedron"): self.edge = edge self.edge_name = edge_name self.volume = volume self.greekname = greekname def scale(self, scalefactor): edge = self.edge * scalefactor # edge unbound to self volume = self.volume * pow(scalefactor, 3) # likewise volume print("DEBUG: a star is born: a new %s" % self.__class__.__name__) return self.__class__(edge = edge, edge_name = self.edge_name, volume = volume, greekname = self.greekname) __mul__ = __rmul__ = scale # e.g. tetra = tetra * 3 def __repr__(self): return "Polyhedron of type %s (vol: %s)" % (self.greekname, self.volume) class Tetra( Poly ): pass class Cube( Poly ): def __init__(self, edge = 1, edge_name = "face diagonal", volume = 3, greekname = "Hexahedron"): Poly.__init__(self, *(edge, edge_name, volume, greekname)) class Octa( Poly ): def __init__(self, edge = 1, edge_name = "edge", volume = 4, greekname = "Octahedron"): Poly.__init__(self, *(edge, edge_name, volume, greekname)) class R_Dodeca( Poly ): def __init__(self, edge = 1, edge_name = "long face diagonal", volume = 6, greekname = "Rhombic dodecahedron"): Poly.__init__(self, *(edge, edge_name, volume, greekname)) class R_Triac( Poly ): def __init__(self, edge = radical(2)/2, edge_name = "long face diagonal", volume = 7.5, greekname = "Rhombic Triacontahedron"): Poly.__init__(self, *(edge, edge_name, volume, greekname)) class Icosa ( Poly ): def __init__(self, edge = 1, edge_name = "edge", volume = 5 * phi**2 * radical(2), greekname = "Icosahedron"): Poly.__init__(self, *(edge, edge_name, volume, greekname)) class Cubocta ( Poly ): def __init__(self, edge = 1, edge_name = "edge", volume = 20, greekname = "Cuboctahedron"): Poly.__init__(self, *(edge, edge_name, volume, greekname))
_______________________________________________ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
