Elliptope

• The space of correlation matrices (positive semi-definite matrices with unit diagonal) define a subset of the unit hypercube called the elliptope.
  
  
• The Hilbert cross-ratio metric can be used to cluster: See Clustering in Hilbert's Projective Geometry: The Case Studies of the Probability Simplex and the Elliptope of Correlation Matrices, 2018.
• We can mesh the elliptope (finite sampling+convex hull) to create a STL file: elliptope3D.stl. This meshed 3D elliptope can be opened using MeshLab, for example.
• One slide explanation:
• Some images of the printed elliptope (thanks to Alexis André for printing the STL file):