FUNDAMENTAL TILINGS

Tiling of the half-plane model by a fundamental domain for SL₂(ℤ). — SL₂(ℤ) PLANE TILING I

Tiling of the disk model by a fundamental domain for SL₂(ℤ). — SL₂(ℤ) DISK TILING I

Tiling of the half-plane model by a fundamental domain for SL₂(ℤ). — SL₂(ℤ) PLANE TILING II

Tiling of the disk model by a fundamental domain for SL₂(ℤ). — SL₂(ℤ) DISK TILING II

Tiling of the half-plane model by a fundamental domain for Γ(2). — Γ(2) PLANE TILING I

Tiling of the disk model by a fundamental domain for Γ(2). — Γ(2) DISK TILING I

Tiling of the half-plane model by a fundamental domain for Γ(2). — Γ(2) PLANE TILING II

Tiling of the disk model by a fundamental domain for Γ(2). — Γ(2) DISK TILING II

Tiling of the half-plane model by a fundamental domain for Γ(2). — Γ(2) PLANE TILING III

Tiling of the disk model by a fundamental domain for Γ(2). — Γ(2) DISK TILING III

Tiling of the half-plane model by a fundamental domain for Γ(2). — Γ(2) PLANE TILING IV

Tiling of the disk model by a fundamental domain for Γ(2). — Γ(2) DISK TILING IV

Tiling of the half-plane model by a fundamental domain for Γ(2). — Γ(2) PLANE TILING V

Tiling of the disk model by a fundamental domain for Γ(2). — Γ(2) DISK TILING V

Tiling of the half-plane model by a fundamental domain for Γ(2). — Γ(2) PLANE TILING VI

Tiling of the disk model by a fundamental domain for Γ(2). — Γ(2) DISK TILING VI

Tiling of the half-plane model by a fundamental domain for Γ(2). — Γ(2) PLANE TILING VII

Tiling of the disk model by a fundamental domain for Γ(2). — Γ(2) DISK TILING VII

Tiling of the half-plane model by a fundamental domain for Γ(2). — Γ(2) PLANE TILING VIII

Tiling of the disk model by a fundamental domain for Γ(2). — Γ(2) DISK TILING VIII

Tiling of the half-plane model by a fundamental domain for Γ(3). — Γ(3) PLANE TILING I

Tiling of the disk model by a fundamental domain for Γ(3). — Γ(3) DISK TILING I

Tiling of the half-plane model by a fundamental domain for Γ(3). — Γ(3) PLANE TILING II

Tiling of the disk model by a fundamental domain for Γ(3). — Γ(3) DISK TILING II

Tiling of the half-plane model by a fundamental domain for Γ(3). — Γ(3) PLANE TILING III

Tiling of the disk model by a fundamental domain for Γ(3). — Γ(3) DISK TILING III

Tiling of the half-plane model by a fundamental domain for Γ(3). — Γ(3) PLANE TILING IV

Tiling of the disk model by a fundamental domain for Γ(3). — Γ(3) DISK TILING IV

Tiling of the half-plane model by a fundamental domain for Γ(3). — Γ(3) PLANE TILING V

Tiling of the disk model by a fundamental domain for Γ(3). — Γ(3) DISK TILING V

Tiling of the half-plane model by a fundamental domain for Γ(3). — Γ(3) PLANE TILING VI

Tiling of the disk model by a fundamental domain for Γ(3). — Γ(3) DISK TILING VI

Tiling of the half-plane model by a fundamental domain for Γ(3). — Γ(3) PLANE TILING VII

Tiling of the disk model by a fundamental domain for Γ(3). — Γ(3) DISK TILING VII

Tiling of the half-plane model by a fundamental domain for Γ(3). — Γ(3) PLANE TILING VIII

Tiling of the disk model by a fundamental domain for Γ(3). — Γ(3) DISK TILING VIII

Tiling of the half-plane model by a fundamental domain for Γ(4). — Γ(4) PLANE TILING I

Tiling of the disk model by a fundamental domain for Γ(4). — Γ(4) DISK TILING I

Tiling of the half-plane model by a fundamental domain for Γ(4). — Γ(4) PLANE TILING II

Tiling of the disk model by a fundamental domain for Γ(4). — Γ(4) DISK TILING II

Tiling of the half-plane model by a fundamental domain for Γ(4). — Γ(4) PLANE TILING III

Tiling of the disk model by a fundamental domain for Γ(4). — Γ(4) DISK TILING III

Tiling of the half-plane model by a fundamental domain for Γ(4). — Γ(4) PLANE TILING IV

Tiling of the disk model by a fundamental domain for Γ(4). — Γ(4) DISK TILING IV

Tiling of the half-plane model by a fundamental domain for Γ(5). — Γ(5) PLANE TILING I

Tiling of the disk model by a fundamental domain for Γ(5). — Γ(5) DISK TILING I

Tiling of the half-plane model by a fundamental domain for Γ(5). — Γ(5) PLANE TILING II

Tiling of the disk model by a fundamental domain for Γ(5). — Γ(5) DISK TILING II

Quaternion algebra tiling in the half-plane model, with a = 7 and b = −1. — Γ PLANE TILING

Quaternion algebra tiling in the disk model, with a = 7 and b = −1. — Γ DISK TILING

Γ is derived from the order ℤ[1, i, j, ij] in the quaternion algebra $(\frac{7, - 1}{ℚ})$ .