Toric objects associated with the dodecahedron
نویسندگان
چکیده
منابع مشابه
The Penrose dodecahedron revisited
This paper gives an elementary account of the ‘‘Penrose dodecahedron,’’ a set of 40 states of a spin3 2 particle used by Zimba and Penrose @Stud. Hist. Phil. Sci. 24, 697–720 ~1993!# to give a proof of Bell’s nonlocality theorem. The Penrose rays are constructed here from the rotation operator of a spin2 particle and the geometry of a dodecahedron, and their orthogonality properties are derived...
متن کاملHidden Symmetries in the Snub Dodecahedron
In a 1979 paper by Coxeter and Huybers [4] , simple formulas were given to construct the snub cube and the snub dodecahedron from the octahedron and the icosahedron respectively , the vertices of the octahedron and icosahedron being the intersection points of certain pairs of edges of the two snub polyhedra . In a later series of papers , Hohenberg [6 , 7 , 8] studied the intersection points of...
متن کاملCMB Anisotropy of the Poincaré Dodecahedron
We analyse the anisotropy of the cosmic microwave background (CMB) for the Poincaré dodecahedron which is an example for a multi-connected spherical universe. We compare the temperature correlation function and the angular power spectrum for the Poincaré dodecahedral universe with the first-year WMAP data and find that this multi-connected universe can explain the surprisingly low CMB anisotrop...
متن کاملA Vanishing Result for Toric Varieties Associated with Root Systems
Consider a root system R and the corresponding toric variety VR whose fan is the Weyl fan and whose lattice of characters is given by the root lattice for R. We prove the vanishing of the higher cohomology groups for certain line bundles on VR by proving a purely combinatorial result for root systems. These results are related to a converse to Mazur’s Inequality for (simply-connected) split red...
متن کاملOn Kepler's Small Stellated Dodecahedron
We give a new geometric computation for the Jacobian of the Riemann surface of genus 4 associated to Kepler’s small stellated dodecahedron. Starting with Threlfall’s description, we introduce several other flat conformal geometries on this surface which are related to holomorphic 1-forms. They allow us to show that the Jacobian is isogeneous to a fourfold product of a single elliptic curve whos...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Filomat
سال: 2020
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil2007329b