The indented path represents the sidereal year of 365.256 days, while the straight path represents the mean solar tropical year of 365.242 days. The base of 4 concave faces could represent hyperbolic geometry as the red region in the center of the hyperbolic Poincare disc. In hyperbolic geometry, as in MInkowski spacetime, time and space are represented differently. That is not the case in elliptic spherical geometry, in which space and time are indistinguishable. Elliptical spherical geometry is the geometry of circles on a sphere, and all the circles look alike.
Hyperbolic geometry is the geometry of a disc whose boundary is a circle.
The timelike things are arcs of circles that are perpendicular to the boundary circle. In higher dimensional spacetime, these arcs would still be 1-dimensional arcs. The spacelike things are circles inside the disc that are tangent to the disc at its boundary circle. They are called horocycles. In higher dimensional spacetime, the horocycles would be spheres instead of circles.