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We consider the problem of determining the length of the shortest pathsbetween points on the surfaces of tetrahedra and cubes. Our approach parallelsthe concept of Alexandrov's star unfolding but focuses on specific polyhedraand uses their symmetries to develop coordinate based formulae. We do so bydefining a coordinate system on the surfaces of these polyhedra. Subsequently,we identify relevant regions within each polyhedron's nets and develop formulaewhich take as inputs the coordinates of the points and produce as an output thedistance between the two points on the polyhedron being discussed.

Landscapes of the Tetrahedron and Cube: An Exploration of Shortest Paths on Polyhedra