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What's it called when a 3D shape can be made of 2D surfaces of all the same size

  1. Apr 9, 2012 #1
    What's it called when a 3D shape can be made of 2D surfaces of all the same shape and dimensions?

    To make a cube, I can use 6 4-sided-squares (of course they're 4 sided)
    To make a pyramid (3 sided), I can use 4 3-sided-triangles

    I can do this with pentagon as well (i don't know what the shape is called)

    Eventually I can't do this as the sides of the shape increase because the remaining angle.


    ... after some thinking I realized I can only do this with 3 equilateral shapes.
    3 sided
    4 sided
    and 5 sided

    MRtiO.png

    Once I get to the hexagon ... well

    r6zJy.png



    Now here's an even more interesting question: Are there any others shapes convex or concave equilateral or not that can be used to create a 3D shape? (where the base shapes remains the same)
    If so how can one determine if a shape is capable of doing this?
     
  2. jcsd
  3. Apr 9, 2012 #2

    turbo

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    Gold Member

    Regular polyhedron
     
  4. Apr 9, 2012 #3
    Thanks!

    Doesn't look like there are too many of those shapes.

    Do you know about the second questions?
     
  5. Apr 9, 2012 #4
    You can use the Euler Formula to prove, if I remember correctly, there are only five which are all regular polygons. 4,6,8,12,20
     
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