FIG. 5: A 2-dimensional cross section of a lopsided neckpinch geometry evolving under RF through the Type-1 singularity. Surgery yields two disconnected 3D ovoids and each becomes spherical under the RF evolution. The resulting geometry is a direct product of two 3-spheres. As the lobed geometry collapses a pinch occurs at t= 183. At this point we remove the axial edges at the pinch and cap each end of the left and right lobe with a new icosahedra. These two surfaces (pre and post surgery) are the 3rd and 4th layers inside the initial surface. After surgery, we remesh both the left and right 3-dimensional ovoids using cubic spline interpolation. This is, to our knowledge, the first numerical realization for PL manifolds of Thurston’s geometrization procedure. This particular surface has 3348 edges, 1580 triangle-based frustum blocks and 960 vertices, although symmetry reduces the number of edges to 80 icosahedral {si} edges and 79 axial {ai} edges.

FIG. 5: A 2-dimensional cross section of a lopsided neckpinch geometry evolving under RF through the Type-1 singularity.
Surgery yields two disconnected 3D ovoids and each becomes spherical under the RF evolution. The resulting geometry is
a direct product of two 3-spheres. As the lobed geometry collapses a pinch occurs at t= 183. At this point we remove the
axial edges at the pinch and cap each end of the left and right lobe with a new icosahedra. These two surfaces (pre and post
surgery) are the 3rd and 4th layers inside the initial surface. After surgery, we remesh both the left and right 3-dimensional
ovoids using cubic spline interpolation. This is, to our knowledge, the first numerical realization for PL manifolds of Thurston’s
geometrization procedure. This particular surface has 3348 edges, 1580 triangle-based frustum blocks and 960 vertices, although
symmetry reduces the number of edges to 80 icosahedral {si} edges and 79 axial {ai} edges.