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

  • Thread starter keysle
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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?
 

Answers and Replies

  • #2
turbo
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Regular polyhedron
 
  • #3
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Thanks!

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

Do you know about the second questions?
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?
 
  • #4
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?

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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