The One Tetrahedron, One Vertex Triangulation of the Solid Torus

Just a quickie… For minimal 1-vertex layered triangulations, one begins with a minimal 1-vertex triangulation of a handlebody (or even a compressionbody, I reckon). For the solid torus – the simplest case – there is just one. …up to homeomorphism of course.

OneTetrahedron-OneVertex-SolidTorus-seethrough (by epsilon_is_afraid_of_zeta)

OneTetrahedron-OneVertex-SolidTorus-GlueBlue (by epsilon_is_afraid_of_zeta)

OneTetrahedron-OneVertex-SolidTorus-edges (by epsilon_is_afraid_of_zeta)

Note that the two blue triangle faces get glued together.
I like how this easily disrupts the familiar angular geometric connotations of a tetrahedron.

~ by Ken Baker on May 15, 2008.

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