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 Post subject: Why are there not more octahedral puzzles?
PostPosted: Tue Apr 08, 2014 8:23 am 
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Joined: Sat Sep 15, 2012 7:42 am
The TwistyPuzzles museum currently has [at least] the following totals:

- 167 157 Tetrahedra
- 165 Cubic Shape Preserving
- 208 Cubic Shapeshifting
- 72 Octahedra
- 122 Dodecahedra
- 67 Icosahedra

My question to designers is: why the low numbers for octahedral puzzles? I can understand the numbers for icosahedral puzzles, since they are the most complicated geometry and are kind of the "last frontier" for platonic geometry, with the series of face-turning puzzles only recently being completed [Jason's Radiolarian series]. Octahedral puzzles have been around since Bandelow's jewel [albeit, with trivial tips removed]. Why are there not more octahedral puzzles? It could be that since the cube and octahedron are duals, many of the octahedral puzzles already have cubic counterparts. But is this all? Or are designers just not interested in octahedral puzzles? Is it something about the geometry that makes them more difficult to work with?

This post is partly motivated by my recent reorganization of my collection. I sorted by shape, but I found that I have only 3 octahedral puzzles, 12ish dodecahedral, 7 tetrahedral, and dozens of cubic.

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Last edited by themathkid on Wed Apr 09, 2014 5:16 am, edited 1 time in total.

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 Post subject: Re: Why are there not more octahedral puzzles?
PostPosted: Tue Apr 08, 2014 5:36 pm 
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I think you nailed it. The cube is the more popular dual brother, so most things happen first in that form, and the octahedral version would be "just a shape mod".

Similar state of affairs for the icosahedron.

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 Post subject: Re: Why are there not more octahedral puzzles?
PostPosted: Wed Apr 09, 2014 1:16 am 
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Where did you get the number for the tetrahedra. I see 159 puzzles in the Four-sided section.

I am afraid 165+208 is even to low for the cube because you could easily count the NxNxNs into it as well.
The tetrahedra section has a lot of mass-produced puzzles.
Besides that I think you are right. Think about Tony Fisher who modified the megaminx into a cube not an octahedron.


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 Post subject: Re: Why are there not more octahedral puzzles?
PostPosted: Wed Apr 09, 2014 5:16 am 
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Andreas Nortmann wrote:
Where did you get the number for the tetrahedra. I see 159 puzzles in the Four-sided section.


Sorry. That should be 157 not 167. Oops. There are 159 four sided puzzles, but two are not tetrahedral.

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Crazy2Face & Crazy3Face Puzzle Spreadsheet
Named 3x3x3 Bandaging Patterns


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