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

[keysle]

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

Once I get to the hexagon ... well

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?

 

[turbo]

Regular polyhedron

 

[keysle]

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?

 

[Fangyang Tian]

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

Once I get to the hexagon ... well

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

 

[blue_raver22]

The term for a 3D shape that can be made of 2D surfaces of all the same size is known as a "uniform polyhedron" or "Platonic solid." This includes shapes such as the cube, pyramid, and dodecahedron.

The term for a 3D shape that can be made of 2D surfaces of all the same shape and dimensions is known as a "regular polyhedron." This includes shapes such as the cube and octahedron.

To determine if a shape is capable of being used to create a 3D shape with all surfaces of the same size or shape, one must examine the angles and sides of the shape. The only shapes that can be used in this manner are those with equilateral sides and angles. This is because the angles must fit together perfectly in order to create a solid 3D shape without gaps or overlaps. Therefore, the shape must have a certain level of symmetry and regularity in its sides and angles to be able to form a uniform or regular polyhedron.