FIG. 4: The RF of a lopsided neckpinch geometry through the Type-1 singularity using surgery and yielding the geometry as a direct product of two 3-spheres. We use axial symmetry of our model to suppress one dimension and the resulting two-lobed geometry can be visualized in Euclidean 3-space (our evolution was fortunately isometrically embeddable in R 3 ). The middle 3’rd and 4’th figure occur at the same time (t = 183.0) in the evolution. They illustrate the explicit manifold surgery, where the spherical caps (two icosahedrons )are placed on the ends of the left and right lobes. This is the first numerical illustration of Thurston’s geometrization procedure that we are aware of. This surface has 3438 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. 4: The RF of a lopsided neckpinch geometry through the Type-1 singularity using surgery and yielding the geometry as
a direct product of two 3-spheres. We use axial symmetry of our model to suppress one dimension and the resulting two-lobed
geometry can be visualized in Euclidean 3-space (our evolution was fortunately isometrically embeddable in R
3
). The middle
3’rd and 4’th figure occur at the same time (t = 183.0) in the evolution. They illustrate the explicit manifold surgery, where
the spherical caps (two icosahedrons )are placed on the ends of the left and right lobes. This is the first numerical illustration
of Thurston’s geometrization procedure that we are aware of. This surface has 3438 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.