Wikipedia:Reference desk/Archives/Mathematics/2018 September 25

= September 25 =

3d closed geometrical figure, 3-sides (that is, surfaces, not lines), all equal
Could a figure fulfill these specs? If not (I imagine it can't), why not? — Preceding unsigned comment added by 31.4.129.90 (talk) 00:40, 25 September 2018 (UTC)


 * Yes you can. https://www.thingiverse.com/thing:2063496 196.213.35.147 (talk) 06:52, 25 September 2018 (UTC)


 * I even know a solid (a 3D figure) which has just one side :) CiaPan (talk) 07:05, 25 September 2018 (UTC)


 * I meant 3 surfaces, flat, closed. Is there a theorem about a figure needing 4 surfaces at least? --82.159.164.102 (talk) 10:55, 25 September 2018 (UTC)


 * @CiaPan. http://ars.userfriendly.org/cartoons/?id=20180104 ;) 196.213.35.147 (talk) 13:03, 25 September 2018 (UTC)
 * According to this, the smallest possible polyhedron is a tetrahedron which has four faces. -- Jayron 32 13:20, 25 September 2018 (UTC)
 * Furthermore, since the OP said "all equal", that's a small closed set known as the platonic solids. In three dimensions, there are only 5 of those in existence: tetrahedron, cube, octahedron, dodecahedron, icosahedron.  That this is a small, closed set of only 5 has been proven since ancient times.  If you include concave polyhedra, you can add the four Kepler–Poinsot polyhedron to the mix, but that's about it.  -- Jayron 32 13:26, 25 September 2018 (UTC)
 * All faces equal isn't enough to make a platonic solid. The 10-sided die used in tabletop gaming is a decahedron with all faces equal.--2404:2000:2000:5:0:0:0:C2 (talk) 23:45, 25 September 2018 (UTC)
 * Fair enough. But you still can't create a 3-flat sided polyhedron.  Of equal faces.  Or of unequal faces.  The smallest number of faces is 4.  -- Jayron 32 02:50, 26 September 2018 (UTC)


 * If you use a toroidal space, a 3D version of a game space where when you leave the bottom of the screen you come in the top and the same for the sides plus extra for the front and back, then three planes can be used to split the space up into parallelepipeds. ;-) I know that's rather pushing things. Dmcq (talk) 11:55, 1 October 2018 (UTC)