Geodesics on the regular tetrahedron and the cube

Diana Davis, Victor Dods, Cynthia Traub, Jed Yang

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Consider all geodesics between two given points on a polyhedron. On the regular tetrahedron, we describe all the geodesics from a vertex to a point, which could be another vertex. Using the Stern–Brocot tree to explore the recursive structure of geodesics between vertices on a cube, we prove, in some precise sense, that there are twice as many geodesics between certain pairs of vertices than other pairs. We also obtain the fact that there are no geodesics that start and end at the same vertex on the regular tetrahedron or the cube.

Original languageEnglish (US)
Pages (from-to)3183-3196
Number of pages14
JournalDiscrete Mathematics
Issue number1
StatePublished - Jan 6 2017
Externally publishedYes


  • Cube
  • Geodesic
  • Regular tetrahedron
  • Stern–Brocot tree

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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