Register to reply

What is a 3-faced 3-D object?

by EnumaElish
Tags: 3faced, object
Share this thread:
EnumaElish
#1
Jan13-08, 09:21 AM
Sci Advisor
HW Helper
EnumaElish's Avatar
P: 2,482
Is there a 3-D object with 3 faces? What is it called?
Phys.Org News Partner Mathematics news on Phys.org
'Moral victories' might spare you from losing again
Fair cake cutting gets its own algorithm
Effort to model Facebook yields key to famous math problem (and a prize)
Ki Man
#2
Jan13-08, 09:32 AM
P: 555
My mind cant comprehend the existence of such a shape
dtl42
#3
Jan13-08, 09:39 AM
P: 117
Thats like asking for a 2 sided 2D object.

dodo
#4
Jan13-08, 09:40 AM
P: 688
What is a 3-faced 3-D object?

A politician?
disregardthat
#5
Jan13-08, 04:31 PM
Sci Advisor
P: 1,742
A cylinder? Or must the faces be flat..?
DaleSpam
#6
Jan13-08, 05:17 PM
Mentor
P: 16,983
No such object exists with flat sides.
ice109
#7
Jan13-08, 05:23 PM
P: 1,705
three lines can only intersect in one point, coincide or be parallel so yes, no such object exists.
Gib Z
#8
Jan13-08, 08:01 PM
HW Helper
Gib Z's Avatar
P: 3,352
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.
uman
#9
Jan13-08, 09:54 PM
P: 352
A tetrahedron with its base removed?
Werg22
#10
Jan13-08, 09:58 PM
P: 1,520
Quote Quote by Gib Z View Post
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?
EnumaElish
#11
Jan13-08, 10:30 PM
Sci Advisor
HW Helper
EnumaElish's Avatar
P: 2,482
Quote Quote by Jarle View Post
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?
Werg22
#12
Jan13-08, 10:42 PM
P: 1,520
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.
Ben Niehoff
#13
Jan13-08, 11:07 PM
Sci Advisor
P: 1,588
Quote Quote by EnumaElish View Post
Is there a 3-D object with 3 faces? What is it called?
A trihedron, of course! :P
Gib Z
#14
Jan14-08, 12:47 AM
HW Helper
Gib Z's Avatar
P: 3,352
Quote Quote by uman View Post
A tetrahedron with its base removed?
Getting the right idea =] No one had stated the shape has to be closed.
masnevets
#15
Jan16-08, 08:36 PM
P: 49
Quote Quote by EnumaElish View Post
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.
rbzima
#16
Jan17-08, 11:55 AM
P: 86
Quote Quote by masnevets View Post
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.
mgb_phys
#17
Jan17-08, 12:38 PM
Sci Advisor
HW Helper
P: 8,954
Wouldn't a Mobius strip have 3 faces? ie. 1 'face' and 2 edges.
dst
#18
Jan17-08, 02:22 PM
P: 389
Quote Quote by mgb_phys View Post
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)


Register to reply

Related Discussions
2-Faced Baby Medical Sciences 7
Jar with an object General Physics 6
Is velocity something an object has or something object experiences? Introductory Physics Homework 2
Object A catches Object B, at when? Introductory Physics Homework 8
What should sex offenders be faced with? Current Events 7