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Problem 72: Polyhedron with Regular Pentagon Faces
- Let M be a closed polyhedral
surface homeomorphic to S2
which is entirely composed of equal regular pentagons.
If M is immersed in 3-space,
is it necessarily the boundary of a union of solid
dodecahedra that are glued together at common facets?
- Richard Kenyon, first posed in 2006.
- Partial and Related Results
- The corresponding question for equal squares has a positive answer.
The question for surfaces embedded in 3-space is also interesting
The Kepler-Poinsot great dodecahedron has regular pentagon
faces, and is immersed, but is not
homeomorphic to S2 (V - E + F = - 6).
- Re-posed at Oberwolfach Workshop, Jan. 2009.
- Entry Revision History
- J. O'Rourke, 23 Jan. 2009.
The Open Problems Project - September 19, 2017