Weeks Manifold

The smallest known closed orientable hyperbolic 3-manifold, with volume ≈0.9427. A finite, negatively-curved universe. Mostow rigidity makes hyperbolic 3-manifolds uniquely rigid: their geometry is fully determined by their topology. Caveat: hyperbolic distances do not embed isometrically into Euclidean ℝ³, so what you see here is a topological schematic, not a faithful geometric rendering of the true Dirichlet domain.

How the boundary is identified: Faces of an irregular fundamental polyhedron are identified by hyperbolic isometries — visualised here only schematically.

3D scene loads on the client.

Universal cover

Last-scattering surface

Radius1.70

Opacity20%

CMB map

Test object

Light rays

Observer view

Compare with

CMB signatures

Matched circles

6 / 9 pair(s)

Identified faces produce pairs of identical temperature circles on the CMB sphere (Cornish-Spergel-Starkman 1998).

Angular separation between paired centres: 55° · Angular radius of each circle: 54° (canonical ≈25°)

Low-l power suppression

C₂ × 62%

Wavelengths longer than the fundamental cell cannot fit. The lowest multipoles are damped relative to flat ΛCDM.

ΛCDMWeeksPlanck / WMAP observed

Schematic temperature map

A Mollweide projection of the sky, with a low-l field aligned along the topology axis. Schematic only.

Preferred axis : θ = 50°, φ = 140°

Summary

CurvatureNegatively curved
OrientableYes
Fundamental-group generators2
Matched circles6 pair(s)
Predicted C₂ suppression39%