Building Euclidean Tilings¶

Pleat can build tilings from by growing rings of prototiles outward from a seed face. These are defined by sets of prototiles which have information on their edges on which tiles to attach (which will again have this information, allowing for iterative growth of the tiling).

This notebook covers:

• the three regular Platonic tilings,
• some Archimedean tilings via convenient factories.

In [1]:

import matplotlib
matplotlib.rcParams['figure.figsize'] = (5, 5)

from pleat import (
    example_graphs,
    example_tilesets,
)
from pleat.rendering import multi_show

import matplotlib matplotlib.rcParams['figure.figsize'] = (5, 5) from pleat import ( example_graphs, example_tilesets, ) from pleat.rendering import multi_show

The three regular tilings¶

platonic(n) returns a list of prototiles that tile the plane regularly for n ∈ {3, 4, 6} (triangles, squares, hexagons).

In [2]:

Gs, names = [], []
for n in [3, 4, 6]:
    G = example_graphs.from_tiles(example_tilesets.platonic(n), rings=3)
    G.recompute_lengths_and_angles()
    Gs.append(G); names.append(f'platonic({n})')
multi_show(Gs, titles=names, face_inset=0.05, render_vertices=False)

Gs, names = [], [] for n in [3, 4, 6]: G = example_graphs.from_tiles(example_tilesets.platonic(n), rings=3) G.recompute_lengths_and_angles() Gs.append(G); names.append(f'platonic({n})') multi_show(Gs, titles=names, face_inset=0.05, render_vertices=False)

Archimedean tilings¶

example_tilesets provides several Archimedean tilings as named factories. Each returns a list of prototiles you pass to from_tiles.

In [3]:

factories = [
    ('3.12.12',     example_tilesets.t_3_12_12),
    ('4.6.12',      example_tilesets.t_4_6_12),
    ('3.3.4.3.4',   example_tilesets.t_3_3_4_3_4),
    ('3.3.3.3.6',   example_tilesets.t_3_3_3_3_6),
]
Gs = []
for _, factory in factories:
    G = example_graphs.from_tiles(factory(), rings=2)
    G.recompute_lengths_and_angles()
    Gs.append(G)
multi_show(Gs, titles=[name for name, _ in factories],
           face_inset=0.05, render_vertices=False, ncols=2)

factories = [ ('3.12.12', example_tilesets.t_3_12_12), ('4.6.12', example_tilesets.t_4_6_12), ('3.3.4.3.4', example_tilesets.t_3_3_4_3_4), ('3.3.3.3.6', example_tilesets.t_3_3_3_3_6), ] Gs = [] for _, factory in factories: G = example_graphs.from_tiles(factory(), rings=2) G.recompute_lengths_and_angles() Gs.append(G) multi_show(Gs, titles=[name for name, _ in factories], face_inset=0.05, render_vertices=False, ncols=2)