Petrial tesseract

The petroid tesseract is a regular skew polychoron consisting of 3 square duocombs. It shares its faces, edges, and vertices with the tesseract, and it has a petrial tetrahedron vertex figure. Its name comes from the fact that its vertex figure is the Petrie dual of the tesseract's vertex figure.

The petroid tesseract is also the only known (concrete) regular polychoron that has duocombs as cells, and is the only possible regular polychoron in 4D space whose vertex figure is the Petrial of a planar polyhedron.

Vertex coordinates
The vertex coordinates of the petroid tesseract are the same as that of it's regiment colonel: the tesseract.