In mathematics, Seifert–Weber space (introduced by Herbert Seifert and Constantin Weber) is a closed hyperbolic 3-manifold.
It is constructed by gluing each face of a dodecahedron to its opposite in a way that produces a closed 3-manifold.
This does not match the 117° dihedral angle of a regular dodecahedron in Euclidean space, but in hyperbolic space there exist regular dodecahedra with any dihedral angle between 60° and 117°, and the hyperbolic dodecahedron with dihedral angle 72° may be used to give the Seifert–Weber space a geometric structure as a hyperbolic manifold.
It is a (finite volume) quotient space of the (non-finite volume) order-5 dodecahedral honeycomb, a regular tessellation of hyperbolic 3-space by dodecahedra with this dihedral angle.
William Thurston conjectured that the Seifert–Weber space is not a Haken manifold, that is, it does not contain any incompressible surfaces; Burton, Rubinstein & Tillmann (2012) proved the conjecture with the aid of their computer software Regina.