Seifert-Weber Dodecahedral Space

A hyperbolic dodecahedral space: opposite pentagonal faces of a regular dodecahedron are identified after a 3/10-turn (108°) twist. The hyperbolic counterpart of the PDS, but with a 108° rather than 36° twist. Caveat: this dodecahedron is rendered in Euclidean ℝ³, but the true Seifert-Weber polyhedron lives in hyperbolic 3-space with dihedral angles of 72°, not the Euclidean ≈116.6°. Mostow rigidity forbids an isometric Euclidean embedding, so what you see is a topological schematic.

How the boundary is identified: Each pentagonal face is glued to the opposite face after a 108° rotation.

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

3 / 6 pair(s)

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

Angular separation between paired centres: 180° · Angular radius of each circle: 50° (canonical ≈30°)

Low-l power suppression

C₂ × 65%

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

ΛCDMSWPlanck / 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 = 65°, φ = 220°

Summary

CurvatureNegatively curved
OrientableYes
Fundamental-group generators6
Matched circles3 pair(s)
Predicted C₂ suppression35%