A plane has no vertex of a regular dodecahedron on it,try to find out how many edges at most may the plane intersect the regular dodecahedron?
Problem
Source: China TST 4 Problem 6
Tags: geometry, 3D geometry, dodecahedron
angiland
23.03.2017 20:13
I have to say I'm surprised to see another solid geometry problem.
Ani10
17.04.2017 12:43
This is actually a cool problem, does anyone have solution or possibly a diagram?
guangzhou-2015
24.04.2017 05:25
I think the answer is 10.But I can't prove it
CJA
01.08.2017 05:24
any one can solve it?
MathLife00
26.10.2017 15:31
guangzhou-2015 wrote: I think the answer is 10.But I can't prove it How? I can't make at most 8.
K_Mirrorheart
03.02.2019 09:55
The answer is $10$ and an easy example could be given by the plane passsing through the dodecahedron's barycentrer parallel to two of its opposite faces(thus intersecting all of its rest $10$ faces). The proof shall be stated later.