Excerpt of a monohedral 11-gon tiling of a non-compact surface embedded in 𝑅³

Credit: Rasmus Direct link: https://mathstodon.xyz/@rasjor/115924337017307626

Excerpt of a monohedral 11-gon tiling of a non-compact surface embedded in 𝑅³. (3 11-gons at every vertex)

The surface splits 𝑅³ in two, so that the space within the dodecagonal tunnels is on one side and the space in the hexagonal tunnels on the other.

The labeled dual edges of the tiling form a partial Cayley surface complex of the group:

G = ⟨ f₁, f₂, f₃, t₁, t₂, t₃, t₄ ∣ f₂², t₃², f₁², t₂², f₃², t₄³, t₁³, (t₁t₄)², f₁t₃t₄⁻¹, f₃t₁⁻¹t₂⁻¹, (f₁f₃)², f₂t₂t₃⁻¹⟩