Prototiles
135 shapesThe individual tile shapes behind the tilings — regular, convex-irregular, star and isotoxal. Star and isotoxal are the two branches of one construction (n points of angle α alternating with β, α + β = 360 − 360/n): reflex β makes a star, convex β makes an isotoxal tile. The Isotoxal (unified) class shows both branches as one α-sorted continuum per side-count — the same 2n-gon walked from convex through β = 180° into a reflex-vertex star. Display-only.
Regular triangle
3 sides
Regular square
4 sides
Regular hexagon
6 sides
Regular octagon
8 sides
Regular dodecagon
12 sides
Side-2 triangle
6 sides
Side-2 square
8 sides
Side-2 hexagon
12 sides
Side-2 dodecagon
24 sides
Side-3 triangle
9 sides
Side-3 square
12 sides
Side-3 hexagon
18 sides
Side-3 dodecagon
36 sides
I-tetromino
10 sides
O-tetromino
8 sides
T-tetromino
10 sides
S-tetromino
10 sides
Z-tetromino
10 sides
J-tetromino
10 sides
L-tetromino
10 sides
cx4-2.4.2.4
4 sides
cx5-2.5.3.3.5
5 sides
cx6-2.5.5.2.5.5
6 sides
cx6-3.4.5.3.4.5
6 sides
cx6-3.5.3.5.3.5
6 sides
cx7-3.5.4.5.3.5.5
7 sides
cx8-3.5.5.5.3.5.5.5
8 sides
cx8-4.4.5.5.4.4.5.5
8 sides
cx8-4.5.4.5.4.5.4.5
8 sides
cx9-4.5.5.4.5.5.4.5.5
9 sides
cx10-4.5.5.5.5.4.5.5.5.5
10 sides
3★ 15°
6 sides
3★ 30°
6 sides
4★ 30°
8 sides
4★ 45°
8 sides
4★ 60°
8 sides
6★ 30°
12 sides
6★ 60°
12 sides
6★ 75°
12 sides
6★ 90°
12 sides
8★ 15°
16 sides
8★ 45°
16 sides
8★ 90°
16 sides
12★ 30°
24 sides
12★ 60°
24 sides
12★ 90°
24 sides
9★ 20°
18 sides
9★ 40°
18 sides
9★ 60°
18 sides
9★ 80°
18 sides
9★ 100°
18 sides
9★ 120°
18 sides
18★ 20°
36 sides
18★ 40°
36 sides
18★ 60°
36 sides
18★ 80°
36 sides
18★ 100°
36 sides
18★ 120°
36 sides
18★ 140°
36 sides
5★ 18°
10 sides
5★ 36°
10 sides
5★ 54°
10 sides
5★ 72°
10 sides
5★ 90°
10 sides
10★ 18°
20 sides
10★ 36°
20 sides
10★ 54°
20 sides
10★ 72°
20 sides
10★ 90°
20 sides
10★ 108°
20 sides
10★ 126°
20 sides
20★ 18°
40 sides
20★ 36°
40 sides
20★ 54°
40 sides
20★ 72°
40 sides
20★ 90°
40 sides
20★ 108°
40 sides
20★ 126°
40 sides
20★ 144°
40 sides
Quadrilateral 15°/165°
4 sides
Quadrilateral 30°/150°
4 sides
Quadrilateral 45°/135°
4 sides
Quadrilateral 60°/120°
4 sides
Quadrilateral 75°/105°
4 sides
Hexagon 75°/165°
6 sides
Hexagon 90°/150°
6 sides
Hexagon 105°/135°
6 sides
Octagon 105°/165°
8 sides
Octagon 120°/150°
8 sides
Dodecagon 135°/165°
12 sides
Hexadecagon 150°/165°
16 sides
Quadrilateral 15°/165°
4 sides
Quadrilateral 30°/150°
4 sides
Quadrilateral 45°/135°
4 sides
Quadrilateral 60°/120°
4 sides
Quadrilateral 75°/105°
4 sides
Hexagon 15°/225°
6 sides
Hexagon 30°/210°
6 sides
Hexagon 45°/195°
6 sides
Hexagon 75°/165°
6 sides
Hexagon 90°/150°
6 sides
Hexagon 105°/135°
6 sides
Octagon 15°/255°
8 sides
Octagon 30°/240°
8 sides
Octagon 45°/225°
8 sides
Octagon 60°/210°
8 sides
Octagon 75°/195°
8 sides
Octagon 105°/165°
8 sides
Octagon 120°/150°
8 sides
Dodecagon 15°/285°
12 sides
Dodecagon 30°/270°
12 sides
Dodecagon 45°/255°
12 sides
Dodecagon 60°/240°
12 sides
Dodecagon 75°/225°
12 sides
Dodecagon 90°/210°
12 sides
Dodecagon 105°/195°
12 sides
Dodecagon 135°/165°
12 sides
Hexadecagon 15°/300°
16 sides
Hexadecagon 30°/285°
16 sides
Hexadecagon 45°/270°
16 sides
Hexadecagon 60°/255°
16 sides
Hexadecagon 75°/240°
16 sides
Hexadecagon 90°/225°
16 sides
Hexadecagon 105°/210°
16 sides
Hexadecagon 120°/195°
16 sides
Hexadecagon 150°/165°
16 sides
Icositetragon 15°/315°
24 sides
Icositetragon 30°/300°
24 sides
Icositetragon 45°/285°
24 sides
Icositetragon 60°/270°
24 sides
Icositetragon 75°/255°
24 sides
Icositetragon 90°/240°
24 sides
Icositetragon 105°/225°
24 sides
Icositetragon 120°/210°
24 sides
Icositetragon 135°/195°
24 sides