Trajectory on a Polyhedron from a Vertex to Itself

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Given a net for a polyhedron, find a straight line from some vertex to itself that lies inside the net. For the regular dodecahedron, such a line exists that does not pass through any other vertex [1]. In this Demonstration, a random net for a polyhedron is given. Drag the locators at the two ends of the red line to try to join the vertex to itself.

Contributed by: Izidor Hafner (March 2019)
Suggested by: Stan Wagon
Open content licensed under CC BY-NC-SA




[1] J. S. Athreya and D. Aulicino, "A Trajectory from a Vertex to Itself on the Dodecahedron," The American Mathematical Monthly, 126(2), 2019 pp. 161–162. doi:10.1080/00029890.2019.1538475.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.