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