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

There are currently 4 programs included with this package:

• sgs.py: Similar grid subdivision of tilings
• balloon.py: Balloon tiling of the sphere
• sgsstats.py: Statistics of the polyhedra/tiling, focused on the use of SGS tilings 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 can be piped together with programs from Antiprism.

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):

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

Visualize a Goldberg polyhedron, with color:

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

Canonical form (no skew faces) of a quadrilateral-faced similar grid subdivision polyhedron:

sgs.py -a 5 -b 3 cube.off | canonical | view_off.py

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

balloon.py 8 -pq | 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]