As the name suggests a TriangleMesh is made out of triangle faces. Your current point collection is organised a little differently. You have all the points, but not all the triangulated faces that make up a shape. Of course it would be possible to determine the triangles, just a little work.

Hemesh has a 1001 possibilities to create shapes. Just look at the endless list of creators. Also the faces do not have to be triangles. For example in this case, you might want to use a FromPolygon creator to create each 5-point-polygon. However when I look at your shape, it looks like a dodecahedron. Hemesh has a HEC_Plato creator that can generate the Platonic solids for you. Explore the available creators, in most cases you probably don't need to feed points manually.

Of course you can also interchange geometry between Toxiclibs and Hemesh. For example Hemesh has a FromToxiTriangleMesh creator and it has many possibilities to generate geometry data.