The boundary and internal edges of a 3D permutahedron.

The 4! vertices are given by the permutations of [1, 3, 4.2, 7], with an edge connecting two vertices if they agree in two of the four coordinates. The 4D vertices live in a 3D hyperplane, namely the sum of the coordinates is 15.2.
Designed with OpenSCAD.

Printed with a raft to ensure adhesion to the bed. Printed without any support using the orientation in the STL file.

Designed with Allen Knutson.