This file tracks how the methods in Pixel2Plex map to the canonical 20 Euclidean 2-uniform tilings from Wikipedia.
References: https://en.wikipedia.org/wiki/2-uniform_tiling
(Also known as demiregular tilings or Grünbaum-Shephard tilings)
| Pixel2Plex | Method | Configuration | Notes |
|---|---|---|---|
| #20 | bi_grandrhombi |
(4.6.12 ; 3.4.6.4) | ✓ Implemented |
| #21 | bi_dodec_snub |
(3.12.12 ; 3.4.3.12) | ✓ Implemented |
| #10 | bi_sq_elongtri_b |
(4⁴ ; 3³.4²)₂ | ✓ Implemented |
| #9 | bi_sq_elongtri_a |
(4⁴ ; 3³.4²)₁ | ✓ Implemented |
| #22 | bi_rhombi_snubhex |
(3.4.6.4 ; 3⁴.6) | ✓ Implemented |
| #0-2 | bi_trihex_a/b/c |
(3.6.3.6 ; 3⁶) | ✓ Custom variants (3) |
| #14 | bi_rhombi_sq |
(3.4.6.4 ; 4⁴) | ✓ Implemented |
| #13 | bi_rhombi_tri |
(3.4.6.4 ; 3⁶) | ✓ Implemented |
| #23 | bi_tri_hexhex |
(3⁶ ; 3².6²) | ✓ Implemented |
| #24 | bi_hexhex_snubhex |
(3².6² ; 3⁴.6) | ✓ Implemented |
| #5 | bi_elongtri_a |
(3⁶ ; 3³.4²)₁ | ✓ Implemented |
| #6 | bi_elongtri_b |
(3⁶ ; 3³.4²)₂ | ✓ Implemented |
| #7 | bi_snubsq_a |
(3³.4² ; 3².4.3.4)₁ | ✓ Implemented |
| #8 | bi_snubsq_b |
(3³.4² ; 3².4.3.4)₂ | ✓ Implemented |
| #25 | bi_tri_snubsq |
(3⁶ ; 3².4.3.4) | ✓ Implemented |
| #3 | bi_snubhex_a |
(3⁶ ; 3⁴.6)₁ | ✓ Implemented |
| #4 | bi_snubhex_b |
(3⁶ ; 3⁴.6)₂ | ✓ Implemented |
| Code | Method | Configuration | Notes |
|---|---|---|---|
| #11 | bi_sq_snubhex |
(4⁴ ; 3⁴.6) | Custom variant: square + snub-hex |
| #12 | bi_snubsq_elongtri |
(3³.4² ; 3².4.3.4) | Custom variant: snub-square + rhombitrihexagonal |
| #15 | bi_snubhex_trihex |
(3⁴.6 ; 3.6.3.6) | Custom variant: snub-hex + trihex |
| #16 | bi_trihex_rhombi |
(3.6.3.6 ; 3.4.6.4) | Custom variant: trihex + rhombitrihex |
| #17 | bi_dodec_grandrhombi |
(3.12² ; 4.6.12) | Custom variant: truncated hexagonal + great rhombitrihex |
| #18 | bi_rhombi_grandrhombi |
(3.4.6.4 ; 4.6.12) | Custom variant: rhombitrihex + great rhombitrihex |
| #19 | bi_dodec_rhombi |
(3.12² ; 3.4.6.4) | Custom variant: truncated hexagonal + rhombitrihex |
- Code uses Wikipedia vertex configuration notation:
(type1 ; type2)with subscripts ₁, ₂ for variants - Internal method names use French descriptive labels:
bi_trihex_a,bi_snubhex_b, etc. - Variants marked with
_1and_2correspond to different symmetry groups
✓ All 20 canonical 2-uniform tilings are implemented
- 7 custom variant tilings beyond the Wikipedia 20
- All tilings use edge-uniform tilings (all edges same length
a) - Custom variant tilings (#11-19) are additional variants mixing canonical vertex types
- Wikipedia: 2-uniform tilings
https://en.wikipedia.org/wiki/2-uniform_tiling - Grünbaum & Shephard (1987): Tilings and Patterns
https://en.wikipedia.org/wiki/Demiregular_tiling