Naked Science Forum

General Science => General Science => Topic started by: imatfaal on 10/03/2011 19:24:46

Title: From 2D to 3D. Can you tell what it is yet?
Post by: imatfaal on 10/03/2011 19:24:46
A Challenge to the NSRers

To explain, the net of a polyhedron is a plane diagram which shows the edges of a polyhedron which could be folded to create the polyhedron.  As shown below the cube has eleven nets

 [ Invalid Attachment ]

Now I see no reason that curved shapes should not have nets too - patterns on a piece of paper that when cut out and the edges are stuck together a three dimensional shape is formed. 

The challenge is - what does the below piece of paper become when taped together.  To be clear (it doesnt show in photo) the paper crosses over itself - ie one section goes under the other where is crosses.  I guarantee it can be put together with no cutting or cheating - just quite a few bits of sellotape; and it makes a proper 3d object that encloses a distinct volume

 [ Invalid Attachment ]

And as a hint - "it's all Geezer's fault"


Title: From 2D to 3D. Can you tell what it is yet?
Post by: Joe L. Ogan on 10/03/2011 20:11:18
Geezer, is someone taking your name in vain?  LOL.  Thanks for comments.  Joe L. Ogan
Title: From 2D to 3D. Can you tell what it is yet?
Post by: RD on 10/03/2011 21:26:44
"prismatic ring (http://imajeenyus.com/mathematics/20040820_prismatic_ring/index.shtml)" ?, or is it a prototype for Prince's "symbol" name (http://en.wikipedia.org/wiki/Love_Symbol_Album) in the 1990's  [:)]

http://mathworld.wolfram.com/PrismaticRing.html
Title: From 2D to 3D. Can you tell what it is yet?
Post by: grizelda on 10/03/2011 21:53:36
A torus wrapped around a wine bottle. Now if we could only get the wine to go on forever.
Title: From 2D to 3D. Can you tell what it is yet?
Post by: Geezer on 10/03/2011 22:16:42
Got it!

It's one of those truss things they advertise in the Sunday Express.
Title: From 2D to 3D. Can you tell what it is yet?
Post by: imatfaal on 11/03/2011 10:39:50
"prismatic ring (http://imajeenyus.com/mathematics/20040820_prismatic_ring/index.shtml)" ?, or is it a prototype for Prince's "symbol" name (http://en.wikipedia.org/wiki/Love_Symbol_Album) in the 1990's  [:)]

http://mathworld.wolfram.com/PrismaticRing.html


Nice One RD! If you have time, I would love to know your thought process - or did you recognize it from a previous example?

 [ Invalid Attachment ]

As you can see it only has one outside face that loops around 3 times and forms a equilateral triangular prismatic ring with a 120deg twist

 [ Invalid Attachment ]


And, of course, it's all Geezers fault because a few weeks ago he asked  can I also make a Mobius thingy with triangular cross section? (http://www.thenakedscientists.com/forum/index.php?topic=37303.msg344094#msg344094)
Title: From 2D to 3D. Can you tell what it is yet?
Post by: Geezer on 15/03/2011 08:15:13
A "few bits of sellotape"! Looks like the whole thing is made of sellotape  [:D]

(I still think the truss idea is better.)