How to construct subgrids of a set of tetrahedron


I have a set of tetrahedron elements and based on these host elements, I want to construct dual-elements around the node with hexahedron sectors. Each sector has eight vertices. The vertices are located at the node, the barycenter of the host element, and barycenter of the three interfaces and the three edges of the host element connected to the node. See figures below.

I don’t find any cell type of VTK for this. Is it possible to construct these cells and assign data on them?

Thanks in advance.