k-uniform tilings, edge-to-edge tilings of regular polygons, can be regrouped as e-isotoxal tilings. 1, 2 and 3-uniform tilings are grouped below.
Counts:
- 1-isotoxal: 4
- 2-isotoxal: 4
- 3-isotoxal: 10
- 4-isotoxal: 13
- 5-isotoxal: 17
- 6-isotoxal: 41
- The 1- to 5-isotoxal edge-homogeneous tilings (40): [1]
- The 6- and 7-isotoxal edge-homogeneous tilings (39): [2]
- The 8- and 9-isotoxal edge-homogeneous tilings (31): [3]
- The 10- to 13-isotoxal edge-homogeneous tilings (40): [4]
- The 14- to 18-isotoxal edge-homogeneous tilings (41): [5]
- The 19- to 29-isotoxal edge-homogeneous tilings (12): [6]
1-isotoxal tilings edit
 36 = {3,6} (k=1, t=1, e=1) |
 63 = {6,3} (k=1, t=1, e=1) |
 (3.6)2 = r{6,3} (k=1, t=2, e=1) |
 44 = {4,4} (k=1, t=1, e=1) |
 (4.4)2 = r{4,4} (k=1, t=2, e=1) |
2-isotoxal tilings edit
 3.122 = t{6,3} (k=1, t=2, e=2) |
 3.4.6.4 = tr{6,3} (k=1, t=3, e=2) |
 4.82 = t{4,4} (k=1, t=2, e=2) |
 32.4.3.4 = s{4,4} (k=1, t=2, e=2) |
3-isotoxal tilings edit
 33.42 (k=1, t=2, e=3) |
 4.6.12 (k=1, t=3, e=3) |
 34.6 (k=1, t=3, e=3) |
 [36; 32.4.3.4] (k=2, t=3, e=3) |
 [3.12.12; 3.4.3.12] (k=2, t=3, e=3) |
 [36; 32.62] (k=2, t=2, e=3) |
 [36; 34.6]1 (k=2, t=3, e=3) |
 [3.6.3.6; 32.62] (k=2, t=2, e=3) |
 [36; 3262; 63] (k=3, t=2, e=3) |
 [36; 346; 3.6.3.6] (k=3, t=3, e=3) |
4-isotoxal tilings edit
 [3.4.6.4; 32.4.3.4] (k=2, t=4, e=4) |
 [3.4.6.4; 33.42] (k=2, t=4, e=4) |
 [4.6.12; 3.4.6.4] (k=2, t=4, e=4) |
 [36; 32.4.12] (k=2, t=4, e=4) | |
 [32.62; 34.6] (k=2, t=2, e=4) |
 [3.42.6; 3.6.3.6]2 (k=2, t=3, e=4) |
 [3.42.6; 3.6.3.6]1 (k=2, t=4, e=4) |
 [44; 33.42]1 (k=2, t=2, e=4) |
 [36; 33.42]1 (k=2, t=3, e=4) |
 [(36)2; 346] (k=3, t=3, e=4) |
 [3262; 3.6.3.6; 63] (k=3, t=2, e=4) |
 [36; 346; 3.6.3.6] (k=3, t=4, e=4) |
 [3.4.6.4; 3.426; 44] (k=3, t=3, e=4) |
5-isotoxal tilings edit
 [3.4.6.4; 3.42.6] (k=2, t=5, e=5) |
 [33.42; 32.4.3.4]1 (k=2, t=4, e=5) |
 [44; 33.42]2 (k=2, t=3, e=5) |
 [36; 33.42]2 (k=2, t=4, e=5) |
 [(36)2; 346] (k=3, t=5, e=5) |
 [36; (324.3.4)2] (k=3, t=4, e=5) |
 [3262; (3.6.3.6)2] (k=3, t=3, e=5) |
 [36; 3342; 324.3.4] (k=3, t=4, e=5) | |
 [3.426; 3.6.3.6; 44] (k=3, t=4, e=5) |
 [3262; 3.6.3.6; 63] (k=3, t=4, e=5) |
 [346; 3262; 63] (k=3, t=2, e=5) |
 [36; 346; 3262] (k=3, t=3, e=5) |
 [36; 3342; 44] (k=3, t=3, e=5) |
6-isotoxal tilings edit
 [(3.4.6.4)2; 3.426] (k=3, t=6, e=6) |
 [36; (346)2] (k=3, t=4, e=6) |
 [3.426; (3.6.3.6)2] (k=3, t=4, e=6) |
 [3.426; (3.6.3.6)2] (k=3, t=5, e=6) |
 [3342; (44)2] (k=3, t=3, e=6) |
 [(3342)2; 44] (k=3, t=4, e=6) |
 [36; (3342)2] (k=3, t=4, e=6) |
 [(36)2; 3342] (k=3, t=5, e=6) |
 [36; 3342; 44] (k=3, t=4, e=6) |
 [36; 3342; 44] (k=3, t=4, e=6) |
 [36; 324.12; 4.6.12] (k=3, t=5, e=6) |
 [324.12; 3.4.6.4; 3.122] (k=3, t=5, e=6) |
 [3.4.3.12; 3.4.6.4; 3.122] (k=3, t=5, e=6) |
 [36; 324.3.4; 324.12] (k=3, t=5, e=6) |
 [346; 3342; 324.3.4] (k=3, t=5, e=6) |
 [36; 324.3.4; 3.426] (k=3, t=5, e=6) |
 [36; 324.3.4; 3.4.6.4] (k=3, t=5, e=6) |
 [36; 3342; 3.4.6.4] (k=3, t=6, e=6) |
 [36; 324.3.4; 3.4.6.4] (k=3, t=6, e=6) |
 [324.3.4; 3.4.6.4; 3.426] (k=3, t=4, e=6) |
 [3342; 324.3.4; 44] (k=3, t=4, e=6) |
 [3.426; 3.6.3.6; 44] (k=3, t=5, e=6) |
 [36; 346; 3262] (k=3, t=3, e=6) |
 [36; 346; 3.6.3.6] (k=3, t=5, e=6) |
7-isotoxal tilings edit
 [36; 34.6]2 (k=2, t=5, e=7) |
 [(346)2; 3.6.3.6] (k=3, t=4, e=7) |
 [(346)2; 3.6.3.6] (k=3, t=4, e=7) |
 [3342; (44)2] (k=3, t=4, e=7) |
 [(3342)2; 44] (k=3, t=5, e=7) |
 [36; (3342)2] (k=3, t=5, e=7) |
 [(36)2; 3342] (k=3, t=6, e=7) |
 [3.426; 3.6.3.6; 4.6.12] (k=3, t=6, e=7) |
 [324.12; 3.4.3.12; 3.122] (k=3, t=4, e=7) |
 [36; 3342; 324.12] (k=3, t=6, e=7) |
 [3.426; 3.6.3.6; 44] (k=3, t=5, e=7) |
 [3.426; 3.6.3.6; 44] (k=3, t=6, e=7) |
 [3262; 3.426; 3.6.3.6] (k=3, t=4, e=7) |
 [3262; 3.426; 3.6.3.6] (k=3, t=5, e=7) |
 [346; 3342; 3.426] (k=3, t=5, e=7) |
 [36; 3342; 44] (k=3, t=5, e=7) |
8-isotoxal tilings edit
 [(3.426)2; 3.6.3.6] (k=3, t=6, e=8) |
 [(3342)2; 324.3.4] (k=3, t=5, e=8) |
 [3342; 324.12; 3.4.6.4] (k=3, t=6, e=8) |
 [3342; 3262; 3.426] (k=3, t=5, e=8) |
 [36; 346; 3262] (k=3, t=5, e=8) |
9-isotoxal tilings edit
 [(36)2; 346] (k=3, t=7, e=9) |
 [3342; (324.3.4)2] (k=3, t=6, e=9) |
References edit
- Chavey, D. (1989). "Tilings by Regular Polygons—II: A Catalog of Tilings". Computers & Mathematics with Applications. 17: 147–165. doi:10.1016/0898-1221(89)90156-9.
- n-uniform tilings Brian Galebach