ABSTRACT
From a polynomial invariant of the binary icosahedral group https://www.w3.org/1998/Math/MathML"> H 3 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq5710.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> due to F. Klein a novel invariant hermitian operator K is constructed. Its complete orthogonal set of invariant eigenstates and eigenvalues quantize H. Poincaré's dodecahedral 3-manifold M with homotopy group https://www.w3.org/1998/Math/MathML"> H 3 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq5711.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . If M is adopted as a model for the space part of the universe, the observed temperature fluctuation of the cosmic microwave background must admit an expansion in these eigenstates.
