After reading about [Easy wireframe display with Barycentric coordinates][3], I started thinking about generating those coordinates uniquely for each vertex.
Is it possible to assign each vertex of an [Apollonian network][1] a single Barycentric coordinate, such that the Barycentric coordinate would be unique for each triangle to which the vertex belongs? For example, a [Triakis Tetrahedron][2] is polyhedron with an Apollonian graph structure.
For instance in the example network here, can a function B(m)
be defined
to give Barycentric coordinates valid for triangles mnp
, mon
, and
mpo
?