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Sam Nead
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One explanation is to look at the "spun triangulation" givingSnapPy gives to the Weeks manifold. This is composed of two ideal tetrahedra with volumes ~0.83828404504 and ~0.10442331774 adding to the familiar ~0.94270736278.

  On the other hand, the given triangulation ofSnapPy gives to the complement of the $5_2$ knot consists of three ideal tetrahedra, all with volume ~0.94270736278. We

We can check that all of thethese various volumes agree by solving the various gluing equations (ensuring (a) that there is no rotation or shearing about edges and ensuring(b) that the cusps are correctly (in)complete).

One explanation is to look at the "spun triangulation" giving the Weeks manifold. This is composed of two ideal tetrahedra with volumes ~0.83828404504 and ~0.10442331774 adding to the familiar ~0.94270736278.

  On the other hand, the given triangulation of the complement of the $5_2$ knot consists of three ideal tetrahedra, all with volume ~0.94270736278. We can check that all of the volumes agree by solving the various gluing equations (ensuring that there is no rotation or shearing about edges and ensuring that the cusps are correctly (in)complete).

One explanation is to look at the "spun triangulation" SnapPy gives to the Weeks manifold. This is composed of two ideal tetrahedra with volumes ~0.83828404504 and ~0.10442331774 adding to the familiar ~0.94270736278. On the other hand, the triangulation SnapPy gives to the complement of the $5_2$ knot consists of three ideal tetrahedra, all with volume ~0.94270736278.

We can check that all of these various volumes agree by solving the gluing equations (ensuring (a) that there is no rotation or shearing about edges and (b) that the cusps are correctly (in)complete).

minor edits.
Source Link
Sam Nead
  • 28.2k
  • 5
  • 72
  • 133

One explanation is to look at the "spun triangulation" giving the Weeks manifold. This is composed of two ideal tetrahedra with volumes ~0.83828404504 and ~0.10442331774 adding to the familiar ~0.94270736278.

On the other hand, the given triangulation of the complement of the $5_2$ knot isconsists of three ideal tetrahedra, all with volume ~0.94270736278. We can check that all of the volumes agree by solving the various gluing equations (coming from theensuring that there is no rotation or shearing about edges and ensuring that the cusps are correctly (in)complete).

One explanation is to look at the "spun triangulation" giving the Weeks manifold. This is composed of two ideal tetrahedra with volumes ~0.83828404504 and ~0.10442331774 adding to the familiar ~0.94270736278.

On the other hand, the given triangulation of the complement of the $5_2$ knot is three ideal tetrahedra, all with volume ~0.94270736278. We can check that all of the volumes agree by solving the various gluing equations (coming from the edges and cusps).

One explanation is to look at the "spun triangulation" giving the Weeks manifold. This is composed of two ideal tetrahedra with volumes ~0.83828404504 and ~0.10442331774 adding to the familiar ~0.94270736278.

On the other hand, the given triangulation of the complement of the $5_2$ knot consists of three ideal tetrahedra, all with volume ~0.94270736278. We can check that all of the volumes agree by solving the various gluing equations (ensuring that there is no rotation or shearing about edges and ensuring that the cusps are correctly (in)complete).

Source Link
Sam Nead
  • 28.2k
  • 5
  • 72
  • 133

One explanation is to look at the "spun triangulation" giving the Weeks manifold. This is composed of two ideal tetrahedra with volumes ~0.83828404504 and ~0.10442331774 adding to the familiar ~0.94270736278.

On the other hand, the given triangulation of the complement of the $5_2$ knot is three ideal tetrahedra, all with volume ~0.94270736278. We can check that all of the volumes agree by solving the various gluing equations (coming from the edges and cusps).