My Math Forum tetrahedron mental illusion(?) help

 Algebra Pre-Algebra and Basic Algebra Math Forum

 September 9th, 2009, 09:12 AM #1 Newbie   Joined: Sep 2009 Posts: 1 Thanks: 0 tetrahedron mental illusion(?) help If you draw a square, and draw lines from all the points, making an cross in the square, you get what looks to me like a tetrahedron. To me it was very interesting because I discovered using a square to get this when I was thinking of how to draw an equilateral tetrahedron. This all stemmed from thought on many other things so things in my mind were overlapping and I realized later that an equilateral tetrahedron can just be drawn by using a triangle, then joining lines from the edges at the center point. I am still confused on whether or not tetrahedron1(with the square) is an equilateral or not. When I look at it, flipping the faces, I think it is. When I look at tetrahedron2(with the triangle) and compare, I cannot understand why I wouldn't be able to move around an actual 3d model of a tetrahedron to have a square outline. Unlike tetrahedron1, tetrahedron2 can use it's base form(the triangle), as the actual base of the tetrahedron. But tetrahedron2, you cannot. Yet it still is possible to see what looks like an equilateral tetrahedron! I don't think it's a 3d right triangle... This was very annoying to write out and sorry for it being annoying to read! draw it yourself, but to get an idea Possibly posted in the wrong place. Please be kind enough to move it instead of deleting it if so mods.
 September 20th, 2009, 05:31 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,464 Thanks: 2038 Using a square, it looks like an octahedron (four faces meeting at each vertex), rather than a tetrahedron (three faces meeting at each vertex).

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