antitile

Manipulation of polyhedra and tilings using Python. This package is designed to work with Antiprism but can be used on its own.

Installation

pip3 install git+git://github.com/brsr/antitile.git

Usage

The package includes a number of scripts. These can be piped together with programs from Antiprism:

• gcopoly.py: The Goldberg-Coxeter subdivision operation of tilings
• balloon.py: Balloon tiling of the sphere
• cellular.py: Colors polyhedra using cellular automata
• nslerp.py: Naive slerp surfaces
• gcostats.py: Statistics of the polyhedra/tiling, focused on the use of GCO to model the sphere (see also off_report in Antiprism)
• view_off.py: A viewer for OFF files using matplotlib, allowing for export to SVG (see also antiview in Antiprism)

These are free-standing:

• breakdown.py: Visualize breakdown structures
• factor.py: Factors Gaussian, Eisenstein, Steineisen (Eisenstein expressed with the 6th root of unity instead of 3rd), and regular integers.

OFF files for the regular icosahedron, octahedron, tetrahedron, cube, and 3- and 4-edged dihedra are included in the data folder in the source.

Examples

Statistics of a geodesic polyhedron (created using what geodesic dome people call Method 1):

gcopoly.py -a 5 -b 3 icosahedron.off | sgsstats.py

Visualize a Goldberg polyhedron, with color:

gcopoly.py -a 5 -b 3 icosahedron.off | off_color -v M -m group_color.txt | pol_recip | view_off.py

Create a quadrilateral-faced similar grid subdivision polyhedron, put it into canonical form (so the faces are all flat), and color it using Conway's Game of Life with random initial condition:

gcopoly.py -a 5 -b 3 cube.off | canonical | off_color test.off -f n | cellular.py -v -b=3 -s=2,3
view_off.py cellular100.off 
# or whatever the last file is if it reaches steady state early

gcopoly.py can subdivide non-orientable surfaces too, at least for Class I and II subdivisions. Here, the base is a Möbius strip-like surface with 12 faces:

unitile2d 2 -s m -w 4 -l 1 | gcopoly.py -a 2 -b 2 -n | view_off.py	

A quadrilateral balloon polyhedra, which happens to resemble a peeled coconut:

balloon.py 8 -pql | view_off.py

For Contributors

This code makes heavy use of vectorized operations on NumPy multidimensional arrays, which are honestly pretty impenetrable until you get familiar with them. (And, uh, even after that.) I use the convention that the last axis of an array specifies the spatial coordinates:

x, y, z = v[..., 0], v[..., 1], v[..., 2]