Open Problems in Discrete Differential Geometry Collected
نویسنده
چکیده
Problem 2 (Richard Kenyon). Let M be a closed polyhedral surface homeomorphic to S 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? The pentagonal faces may intersect each other (and the “union of solid dodecahedra” must be defined appropriately) but two different faces are not allowed to coincide. (The corresponding question for equal squares has an affirmative answer.)
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تاریخ انتشار 2009