Timeline for Are there Monohedra with odd numbers of faces?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Jan 5 at 0:33 | history | edited | LSpice | CC BY-SA 4.0 |
Consistent plurals, while this is on the front page
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| Jan 5 at 0:22 | answer | added | Oscar Lanzi | timeline score: 0 | |
| S Feb 27, 2022 at 13:56 | vote | accept | Nandakumar R | ||
| Feb 24, 2022 at 14:16 | answer | added | user3816 | timeline score: 7 | |
| Jan 14, 2022 at 12:16 | vote | accept | Nandakumar R | ||
| S Feb 27, 2022 at 13:56 | |||||
| Oct 17, 2021 at 16:37 | comment | added | Nandakumar R | Thanks for pointing this out, Prof Eppstein. | |
| Oct 17, 2021 at 8:01 | comment | added | David Eppstein | To add to M. Winter's comment: the four edges of the face cannot include an edge whose length is unique, because then pairs of faces would have to be matched across these edges and the total number of faces would have to be even. Together with the impossibility of centrally symmetric faces that means that the only possible face shapes are kites. | |
| Oct 16, 2021 at 21:40 | answer | added | Yaakov Baruch | timeline score: 10 | |
| Oct 14, 2021 at 8:27 | comment | added | Nandakumar R | Thanks Bill Bradley for the intro to Szilassi polyhedron. I hadn't thought about polyhedra that are not simply connected. But this is a very interesting object - although the faces are not congruent! And thanks M Winter for your analysis; however, I am unable to visualize or draw a polyhedron with odd number of faces and all faces being mutually congruent and non-centrally symmetric quadrangles. | |
| Oct 13, 2021 at 13:04 | comment | added | M. Winter | Considering the dual of the edge-graph, using the hand-shaking-lemma and that there must be a vertex of degree at most 5, we see that the only option for an odd number of faces is if the monohedron has quadrangle faces. The faces can also not be centrally symmetric as otherwise the whole polyhedron would be a centrally symmetric zonohedron, having even many faces. | |
| Oct 13, 2021 at 12:52 | comment | added | Bill Bradley | This violates a few of your conditions, but you may find the 7-faced Szilassi polyhedron interesting: en.wikipedia.org/wiki/Szilassi_polyhedron | |
| Oct 13, 2021 at 10:04 | history | asked | Nandakumar R | CC BY-SA 4.0 |