Online since 2002. Over 3300 puzzles, 2600 worldwide members, and 270,000 messages.

TwistyPuzzles.com Forum
 It is currently Wed Mar 12, 2014 10:24 am

 All times are UTC - 5 hours

 Page 1 of 1 [ 7 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: Dino truncated triakis tetrahedron? (idea)Posted: Thu Jul 18, 2013 3:03 am

Joined: Fri Nov 05, 2010 2:20 am
Location: Wherever

It seems that the 3 fold pentagon corners could be left unfudged, but how much fudging would be needed to turn the hexagon-pentagon-pentagon vertexes into 3 fold symmetric corners?

Also, what is the dual of this solid? Wikipedia mentions 'hexakis truncated tetrahedron', but what does this look like? I cant visualise it, and I cant find it.

_________________
A budding puzzle designer!

Check out my Shapeways shop!

Top

 Post subject: Re: Dino truncated triakis tetrahedron? (idea)Posted: Thu Jul 18, 2013 4:32 am

Joined: Sun Oct 08, 2006 1:47 pm
Location: Houston/San Antonio, Texas
I suspect that is indeed possible, but I have yet to identify the best way to create the geometry for fudged puzzles, Oskar seems to be the champ at that! He made the Illegal Cube work, and it seems like it should require more fudging than this.

It is worth mentioning that a few puzzles have used this shape before.

First was Timur's Skyglobe, which turns about the hexagonal faces - although fudged, this puzzle does not jumble
Then came David Pitcher's Jumball, which turns about the irregular pentagonal faces, making it a jumbling puzzle

The dual, by the way, looks like this:
Attachment:

TruncatedTriakisTetrahedronDual.png [ 23.3 KiB | Viewed 654 times ]

It looks a lot like an icosahedron at first, but notice that there is one point in view where 6 triangles meet at a corner, instead of the usual 5. There are 28 faces and 16 points. 4 of those points are surrounded by 6 triangles, the rest by 5 triangles (exaclty one of which is regular). There are 4 regular triangles and the other 24 are all the same isosceles triangle: approx 64.55, 64.55, 52.89 degrees. Looking at it after being so used to seeing icosahedrons is a little off-putting, you can feel that the geometry is slightly off but it takes a little effort to conciously spot the illegal 6-fold symmetries (local only, the global symmetry is only 3-fold). It is a bit reminiscent of a Geodesic dome, though I am not sure if it has a specific name - I was unable to find it on Wikipedia.

Using the Conway Polyhedron Notation, I believe it should be called a Hexakis Truncated Tetrahedron

You should ask Oskar to make it!

Peace,
Matt Galla

Last edited by Allagem on Thu Jul 18, 2013 5:05 am, edited 2 times in total.

Top

 Post subject: Re: Dino truncated triakis tetrahedron? (idea)Posted: Thu Jul 18, 2013 4:54 am

Joined: Sun Mar 15, 2009 12:00 am
Location: Jarrow, England
Since the pentagons on the Truncated triakis tetrahedron are irregular, when you constructed the points for the dual, how did you find the "centre" of these pentagonal faces?

_________________
My Shapeways Shop: http://www.shapeways.com/shops/gus_shop

Top

 Post subject: Re: Dino truncated triakis tetrahedron? (idea)Posted: Thu Jul 18, 2013 4:58 am

Joined: Fri Nov 05, 2010 2:20 am
Location: Wherever
Gus wrote:
Since the pentagons on the Truncated triakis tetrahedron are irregular, when you constructed the points for the dual, how did you find the "centre" of these pentagonal faces?

I don't know what program Allagem uses, but for me, solidworks has a 'point' feature which creates a point bases on references. You can choose the face and it (somehow) calculated the center.

More on topic, the mechanism for the puzzle probably will not be incredibly hard to do. It is the fudging that is the tricky part. Just guessing.

_________________
A budding puzzle designer!

Check out my Shapeways shop!

Top

 Post subject: Re: Dino truncated triakis tetrahedron? (idea)Posted: Thu Jul 18, 2013 5:10 am

Joined: Sun Oct 08, 2006 1:47 pm
Location: Houston/San Antonio, Texas
Gus wrote:
Since the pentagons on the Truncated triakis tetrahedron are irregular, when you constructed the points for the dual, how did you find the "centre" of these pentagonal faces?

That's not the only way of creating a dual
The dual is also the surface bounded by the planes perpendicular to the lines from the center of the puzzle to each vertex, aligned to intersect that vertex

By the way, I am using the program Cabri 3D. It is essentially a 3-D version of using a straight edge and compass on a computer, as it can only perform basic geometric manipulations, but if you can identify midpoints, rotations, circles, perpendicular planes, spheres, or other simple geometry and their intersections to define the shape you wish to make it can generate some nice sketches with relatively little effort. It cannot handle any sort of cutting or extruding though - it isn't a real CAD program, just geometry!

Peace
Matt Galla

Top

 Post subject: Re: Dino truncated triakis tetrahedron? (idea)Posted: Thu Jul 18, 2013 5:36 am

Joined: Sun Mar 15, 2009 12:00 am
Location: Jarrow, England
Interesting software Matt. I knew there would be a sneaky (meaning: correct) mathematical way of making the dual. By the way, according to this site there is more than one way of creating the TTT - which one is best for our purposes?

_________________
My Shapeways Shop: http://www.shapeways.com/shops/gus_shop

Top

 Post subject: Re: Dino truncated triakis tetrahedron? (idea)Posted: Thu Jul 18, 2013 6:10 am

Joined: Fri Nov 05, 2010 2:20 am
Location: Wherever
Gus wrote:
Interesting software Matt. I knew there would be a sneaky (meaning: correct) mathematical way of making the dual. By the way, according to this site there is more than one way of creating the TTT - which one is best for our purposes?

The one that produces the closest to 3 fold hexagon-pentagon-pentagon vertexes.

_________________
A budding puzzle designer!

Check out my Shapeways shop!

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 7 posts ]

 All times are UTC - 5 hours

#### Who is online

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot post attachments in this forum

Search for:
 Jump to:  Select a forum ------------------ Announcements General Puzzle Topics New Puzzles Puzzle Building and Modding Puzzle Collecting Solving Puzzles Marketplace Non-Twisty Puzzles Site Comments, Suggestions & Questions Content Moderators Off Topic