# How would you suggest to construct this object?

• posted on June 29, 2006, 10:22 pm

I'm sorry, but I don't have a picture for this problem. I hope I can describe it clearly.
Suppose you have two cubes, one 3" on a side, and the other slightly larger, say like 3.1" on a side.
The problem is to drill a hole through the SMALLER cube such that the larger cube can pass through the smaller cube, through the hole.
If you take the smaller cube and hold it between your index finger and thumb, holding it at opposite vertices (the major diagonal of the cube), you can see but twirling the cube to the right angle that from this perspective, it's cross-section is a hexagon.
It just happens that the hexagonal cross-section of a 3" cube is in fact large enough to drill a square hole through it that would pass a 3.1" square.
So my problem ... HOW do I possibly construct this beast? What I need to do is take a cube and drill a hole through it at this strange angle. Then I need to "square" the hole, making it clean enough to let the larger cube pass through it.
It's a really neat math construct that is great to show to high school kids. Anyone have any ideas how I would approach making this?
Jack

<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
• posted on June 29, 2006, 11:01 pm
On Thu, 29 Jun 2006 16:22:32 -0600, "mywebaccts (at) PLUGcomcast.net" <"mywebaccts (at) PLUGcomcast.net"> wrote:

It should not be difficult to jig this for a drill press/morticer. Build an angled auxillary table at the "strange angle", which if you're teaching this I hope you know what it is ;) Then attach another piece with a 90 degree notch but at 45 degrees to hold the cube in place. That will let you drill a hole. You can use the same setup to hold the cube while you hold your chisel vertically.
I agree with the other poster though, it'd be easier to assemble it out of 6 precut sides, but not as nice of a visual aid.
-Leuf

<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
• posted on June 30, 2006, 2:41 am

Don't start with a cube; start with stock that's much larger and drill out the hole first. Then slice off the stock that is beyond the boundaries of the cube. Just take care that you orient the hole, or your cuts, appropriately. What's left is your finished cube.
- Owen -

<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
• posted on July 1, 2006, 1:26 am
Yeah, what Owen said.
-Zz
On Thu, 29 Jun 2006 22:41:20 -0400, "Owen Lawrence"

<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
• posted on June 30, 2006, 5:32 pm
On Thu, 29 Jun 2006 16:22:32 -0600, "mywebaccts (at) PLUGcomcast.net" <"mywebaccts (at) PLUGcomcast.net"> wrote:

You can't drill this, you have to bore it.
A "drill" is a self-guided tool for cutting holes. "Boring" (in workshop terms) is a different process - you clamp it rigidly to a rigid machine, then you rotate a single point cutter so as to cut the hole. The difference is that the tool is guided by the rigidity of the frame and machine, not a rubbing contact on the tool.
Find someone with a milling machine (most engineering workshops), make up a 3-pointed stand to support it and away you go.

<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
• posted on June 30, 2006, 9:43 pm
I like the reverse-engineering approach. Surround a hole with wood fragments that form a cube. Similar to hunting elephants in Africa - examine all animals, retaining those whose exterior surface is that of an elephant.

<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
• posted on July 1, 2006, 1:27 am
Yeah, what Andy said.
-Zz
On Fri, 30 Jun 2006 18:32:31 +0100, Andy Dingley

<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
• posted on June 30, 2006, 6:14 pm
Mike Richardson wrote:

Here's some more math for all and another view of the cube.
http://mathworld.wolfram.com/PrinceRupertsCube.html

<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
• posted on July 1, 2006, 3:37 pm
Thanks again to everyone for their help. I'll probably "cheat" with the paper model first, if not only to help better visualize the final product. Then I think I'll try a jig approach. I don't know anyone with a mill and I'm not looking for a 'perfect' rendition, just one good enough to help confound and convince the kids of the beauty of math!
Jack
mywebaccts (at) PLUGcomcast.net wrote: