Wikipedia:Reference desk/Archives/Mathematics/2022 April 27

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April 27

Possible quadrilaterals from slicing a Tetrahedron?

What are the boundary conditions of possible quadrilaterals from slicing a tetrahedron. I *think* they have to be convex *and* no angle can be smaller than 60 degrees, is that correct? (and every triangle is possible).Naraht (talk) 12:53, 27 April 2022 (UTC)

Followup

Any idea on the boundary conditions for the possible cross sections of the other regular solids? For example, you can get a regular hexagon from slicing a Cube and a regular decagon from slicing a Dodecahedron or an Icosahedron, but you can't get a regular Nonagon. I have *no* idea how to figure out what Nonagons are possible from slicing a regular solid.Naraht (talk) 12:53, 27 April 2022 (UTC)

As to the first question, basically the same question was embedded in Wikipedia:Reference desk/Archives/Mathematics/2021 March 27 § Possible Cross Sections of the Regular polyhedra. There was some confusion then if you meant "regular tetrahedron".  --Lambiam 20:42, 27 April 2022 (UTC)