What is a 3-faced 3-D object?


by EnumaElish
Tags: 3faced, object
EnumaElish
EnumaElish is offline
#1
Jan13-08, 09:21 AM
Sci Advisor
HW Helper
EnumaElish's Avatar
P: 2,483
Is there a 3-D object with 3 faces? What is it called?
Phys.Org News Partner Mathematics news on Phys.org
Researchers help Boston Marathon organizers plan for 2014 race
'Math detective' analyzes odds for suspicious lottery wins
Pseudo-mathematics and financial charlatanism
Ki Man
Ki Man is offline
#2
Jan13-08, 09:32 AM
P: 555
My mind cant comprehend the existence of such a shape
dtl42
dtl42 is offline
#3
Jan13-08, 09:39 AM
P: 117
Thats like asking for a 2 sided 2D object.

dodo
dodo is offline
#4
Jan13-08, 09:40 AM
P: 688

What is a 3-faced 3-D object?


A politician?
disregardthat
disregardthat is online now
#5
Jan13-08, 04:31 PM
Sci Advisor
P: 1,683
A cylinder? Or must the faces be flat..?
DaleSpam
DaleSpam is offline
#6
Jan13-08, 05:17 PM
Mentor
P: 16,469
No such object exists with flat sides.
ice109
ice109 is offline
#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
Gib Z is offline
#8
Jan13-08, 08:01 PM
HW Helper
Gib Z's Avatar
P: 3,353
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
uman is offline
#9
Jan13-08, 09:54 PM
P: 352
A tetrahedron with its base removed?
Werg22
Werg22 is offline
#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
EnumaElish is offline
#11
Jan13-08, 10:30 PM
Sci Advisor
HW Helper
EnumaElish's Avatar
P: 2,483
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
Werg22 is offline
#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
Ben Niehoff is offline
#13
Jan13-08, 11:07 PM
Sci Advisor
P: 1,562
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
Gib Z is offline
#14
Jan14-08, 12:47 AM
HW Helper
Gib Z's Avatar
P: 3,353
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
masnevets is offline
#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
rbzima is offline
#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
mgb_phys is offline
#17
Jan17-08, 12:38 PM
Sci Advisor
HW Helper
P: 8,961
Wouldn't a Mobius strip have 3 faces? ie. 1 'face' and 2 edges.
dst
dst is offline
#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