Dodecahedron universe after PLanck
Hi Wabbit, you got me to look up the relevant 2015 Planck release.http://arxiv.org/pdf/1502.01593v1.pdfPlanck 2015 results. XVIII. Background geometry and topology of the Universe
I couldn't find the page where it discussed or constrained the dodecahedral idea, but I found these references at the end. So presumably it must discuss that somewhere in the 21 page article.
Lachieze-Rey, M. & Luminet, J., Cosmic topology. 1995, Physics Reports, 254, 135
Lehoucq, R., Lachieze-Rey, M., & Luminet, J. P., Cosmic crystallography. 1996, A&A, 313, 339, arXiv:gr-qc/9604050
Lew, B. & Roukema, B., A test of the Poincare ́ dodecahedral space topology hypothesis with the WMAP CMB data. 2008, A&A, 482, 747, arXiv:0801.1358
Luminet, J.-P., Weeks, J. R., Riazuelo, A., Lehoucq, R., & Uzan, J.-P., Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background. 2003, Nature, 425,
Haven't seen much about that beautiful Luminet idea recently. Johannes Kepler was enchanted by the platonic solids. http://en.wikipedia.org/wiki/Johannes_Kepler#Mysterium_Cosmographicum