Third-turn flat three-manifold
= Third-turn flat three-manifold
The <mapping torus> of an order-three rotation of a hexagonal <flat torus> is a closed orientable <flat Riemannian manifold> with holonomy $C_3$. A screw rotation through $2\pi/3$ with axial displacement $1/3$, together with the planar lattice, describes its deck group. Its first <Betti number> is one.