Exploring 3-D Objects: The Definition and Properties of Three-Dimensional Shapes

  • Thread starter EnumaElish
  • Start date
In summary, the conversation discussed the existence of a 3-D object with 3 faces. It was determined that there is no such object with flat surfaces, but a Mobius strip is an example of a 2-sided 3-D object. The minimum number of faces for a 3-D object is n+1, with a tetrahedron being the simplest example. It was also mentioned that a definition of a 3-D object is necessary to fully answer the question.
  • #1
EnumaElish
Science Advisor
Homework Helper
2,350
124
Is there a 3-D object with 3 faces? What is it called?
 
Mathematics news on Phys.org
  • #2
My mind can't comprehend the existence of such a shape :redface:
 
  • #3
Thats like asking for a 2 sided 2D object.
 
  • #4
A politician?
 
  • #5
A cylinder? Or must the faces be flat..?
 
  • #6
No such object exists with flat sides.
 
  • #7
three lines can only intersect in one point, coincide or be parallel so yes, no such object exists.
 
  • #8
There is an infinite number of 3 dimensional objects with 3 faces, just as there are an infinite number 2 dimensional objects with 2 sides.
 
  • #9
A tetrahedron with its base removed?
 
  • #10
Gib Z said:
There is an infinite number of 3 dimensional objects with 3 faces, just as there are an infinite number 2 dimensional objects with 2 sides.

Playing Captain Obvious these days? :tongue2:
 
  • #11
Jarle said:
A cylinder? Or must the faces be flat..?
Good answer; but I was asking about flat surfaces. I understand that no such object exists. Is there a theorem about the min. number of flat surfaces that a 3-D object must have?
 
  • #12
I think it's best we first clarify what a closed 3 dimensional object is for our purposes. I would say that a simple closed 3 dimensional object is a collection of planar surfaces with properties among which is that a surface in that collection connects to at least as many surfaces as it has vertices. The simplest planar figure is the triangle; since it has 3 sides, it is not possible to meet the said property with only 3 planar faces, hence there is no such 3 dimensional object.
 
Last edited:
  • #13
EnumaElish said:
Is there a 3-D object with 3 faces? What is it called?

A trihedron, of course! :P
 
  • #14
uman said:
A tetrahedron with its base removed?

Getting the right idea =] No one had stated the shape has to be closed.
 
  • #15
EnumaElish said:
Good answer; but I was asking about flat surfaces. I understand that no such object exists. Is there a theorem about the min. number of flat surfaces that a 3-D object must have?

Hello,

What you are thinking of is a 3 dimensional (convex) polytope. I assume you mean codimension 1 faces (i.e. 2 dimensional faces). Technically, edges and vertices are also called faces. In this case, the minimum number of faces is 4 (a tetrahedron). In general, an n dimensional polytope needs to have at least n+1 facets.
 
  • #16
masnevets said:
Hello,

What you are thinking of is a 3 dimensional (convex) polytope. I assume you mean codimension 1 faces (i.e. 2 dimensional faces). Technically, edges and vertices are also called faces. In this case, the minimum number of faces is 4 (a tetrahedron). In general, an n dimensional polytope needs to have at least n+1 facets.

Darn, I was going to say that. Furthermore, when you consider the convex hull of this polytope, the convex hull can extend in two dimensions; but there needs to be at least one point above the plane of the other points in order to achieve what you desire. Otherwise it's simply a 2-dimensional face.
 
  • #17
Wouldn't a Mobius strip have 3 faces? ie. 1 'face' and 2 edges.
 
  • #18
mgb_phys said:
Wouldn't a Mobius strip have 3 faces? ie. 1 'face' and 2 edges.

Good thinking. Why wouldn't it? Make the edges thicker = 3 faces.

But obviously no flat surfaced object could have 3 faces. (politicians aside)
 
  • #19
Are there geometries where such an object could be constructed or is that a silly question to ask?
 
  • #20
mgb_phys said:
Wouldn't a Mobius strip have 3 faces? ie. 1 'face' and 2 edges.

It only has 1 'face' and 1 edge though. And a Möbius strip is 2-dimensional (as a manifold).
 
  • #21
Of course - the edges are connected - dumb of me.
So it's possible to have a 2 sided 3D object but not a 3 sided one ?
 
  • #22
mgb_phys said:
Of course - the edges are connected - dumb of me.
So it's possible to have a 2 sided 3D object but not a 3 sided one ?
A cylinder has 3 sides if you include it's curved surface. Both 'sides' of a mobius strip are curved into each other so you only have 2 sides. With only flat surfaces I think n+1 is the minimum number.
 
  • #23
just start with a closed 3 dimensional object like a sphere. then triangulate it with three faces, using curved edges of course.
 
  • Like
Likes Slola
  • #24
actually i am not sure what you mean by three dimensional object as i have described a 2 dimensional manifold. a three dimensional object should have some 3 dimensional faces.

i guess i thought you meant a closed surface that does not embed in 2 space, which is the lay persons notion of a three dimensional object.

so to answer the question we need a definition of a three dimensional object.

i guess i could modify ,my example by taking the cone over it with vertex at the center of the sphere, i.e. make it into a ball example.
 
Last edited:

What is a 3-faced 3-D object?

A 3-faced 3-D object is a three-dimensional object that has three flat surfaces, also known as faces. These faces are typically in the shape of polygons, such as triangles, squares, or rectangles.

What is the difference between a 3-faced 3-D object and a regular 3-D object?

The main difference between a 3-faced 3-D object and a regular 3-D object is the number of faces. Regular 3-D objects typically have more than three faces, while 3-faced 3-D objects only have three.

Can a 3-faced 3-D object exist in the real world?

Yes, a 3-faced 3-D object can exist in the real world. Some examples of 3-faced 3-D objects include pyramids, triangular prisms, and triangular pyramids.

What is the name of the shape of a 3-faced 3-D object?

The shape of a 3-faced 3-D object is typically referred to as a triangular-based pyramid or a triangular prism. This is because the three faces are typically in the shape of triangles.

How can you determine the volume of a 3-faced 3-D object?

The volume of a 3-faced 3-D object can be determined by using the formula V = (1/3) * b * h, where b is the area of the base and h is the height of the object. The volume of a triangular-based pyramid can be calculated using the formula V = (1/3) * b * h, while the volume of a triangular prism can be calculated using the formula V = b * h, where b is the area of the base and h is the height of the object.

Similar threads

Replies
3
Views
1K
  • General Math
Replies
23
Views
1K
Replies
2
Views
4K
Replies
1
Views
436
Replies
3
Views
1K
Replies
4
Views
528
  • General Math
Replies
1
Views
875
  • Special and General Relativity
2
Replies
37
Views
2K
Replies
2
Views
1K
  • Sci-Fi Writing and World Building
Replies
3
Views
631
Back
Top